Optimal Inverter VAR Control in Distribution Systems with High PV Penetration

Contents

Problem Formulation

The aim of the study is to demonstrate the benefits of inverter reactive power control to mitigate the rapid and large voltage fluctuations due to the high penetration of photovoltaic generation and the resulting reverse power flow.

Proposed Solution

The approach for this problem is formulated as a radial optimal power flow (OPF) to minimiza the loss and energy consumptions, subject to constraints on voltage magnitudes.

A minimization of power loss is formulated as in the paper page 4, equation (17), which considers the line losses as the first part, the Conservation Voltage Reduction effects (CVR) as the second part, and the losses in the inverter due to reactive power fow as the thord part.

The minimization problem is subjected to a bunch of voltage and power contraint in the while system, which consists of all the power, current, and voltage equations, which are shown in the paper page 4, equation (18)-(27).

Tn ths study, first, we investigate the interaction between the solar plant reactive power, active power, and overall load under the voltage constraint.

In this algorithm operation, we first intialize all the system parameters, then real-life data from South California Edison (SCE) company are applied to do the simulation. The optimization algorithm is solved by the CVX solver.

System parameter initialization

First, all the parameters will be initiallized to provide a general picture of the problem.

pcs=[0.2 0.3 0.4];              % loop value for system load
pgs_45 = [1:0.5:4];           % input parameter of PV real power injection
qgs_45 = zeros(size(pgs_45));

for pc_s=1:3

for pg_i = 1:7

i_total=56;                 % define system size
j_total=56;

pc=zeros(i_total,1);         % real power demand
qc=zeros(i_total,1);         % reactive power demand
sc=zeros(i_total,1);         % total power demand
qsc=zeros(i_total,1);        % shunt capacitor vector
pg=zeros(i_total,1);         % real power generated by PVs and inverters
qg=zeros(i_total,1);         % reactive power generated by PVs and inverters

r=zeros(i_total,j_total);    % the line resistance
x=zeros(i_total,j_total);    % the line reactance

l=zeros(i_total,j_total);    % current relaxation
v=12*ones(i_total,1);        % voltage relaxation
s=zeros(i_total,1);          % power relaxation
t=zeros(i_total,1);

alpha=zeros(i_total,1);      % CVR coefficient
cv=ones(i_total,1);          % inverter loss coefficients
cr=ones(i_total,1);
qg_max=zeros(i_total,1);     % optimization constraints parameters
V_min=zeros(i_total,1);
V_max=zeros(i_total,1);
pc_min=zeros(i_total,1);
qc_min=zeros(i_total,1);

P=zeros(i_total,j_total);    %real power flow
Q=zeros(i_total,j_total);    %reactive power flow
E=zeros(i_total,j_total);    %network connection (graph arc)

Data import of the simulation

In this study, we input the historical SCADA data from SCE company into a chosen SCE's 56-node distribution feeders with very high penetration of photovoltaics.

E(1,2)=1;                   % E Matrix, imply the connection between each node, 1:connected, 0: open
E(2,3)=1;
E(2,4)=1;
E(4,5:7)=1;
E(7,8)=1;
E(8,9:10)=1;
E(10,11)=1;
E(11,12:13)=1;
E(13,14:15)=1;
E(15,16:17)=1;
E(17,18)=1;
E(18,19)=1;
E(4,20)=1;
E(20,21)=1;
E(21,22)=1;
E(20,23)=1;
E(23,24:25)=1;
E(25,26)=1;
E(26,27)=1;
E(27,28)=1;
E(28,29)=1;
E(29,30)=1;
E(30,31)=1;
E(26,32)=1;
E(32,33)=1;
E(32,34)=1;
E(34,35:36)=1;
E(36,37)=1;
E(34,38)=1;
E(38,39)=1;
E(39,40)=1;
E(34,41)=1;
E(41,42)=1;
E(42,43:46)=1;
E(41,47)=1;
E(47,48:49)=1;
E(49,50:51)=1;
E(51,52:53)=1;
E(53,54:56)=1;


r(1,2)=0.16;             % r matrix, imply network resistances
r(2,3)=0.824;
r(2,4)=0.144;
r(4,5)=1.026;
r(4,6)=0.741;
r(4,7)=0.528;
r(7,8)=0.358;
r(8,9)=2.032;
r(8,10)=0.502;
r(10,11)=0.372;
r(11,12)=1.431;
r(11,13)=0.429;
r(13,14)=0.671;
r(13,15)=0.457;
r(15,16)=1.008;
r(15,17)=0.153;
r(17,18)=0.971;
r(18,19)=1.885;
r(4,20)=0.138;
r(20,21)=0.251;
r(21,22)=1.818;
r(20,23)=0.225;
r(23,24)=0.127;
r(23,25)=0.284;
r(25,26)=0.171;
r(26,27)=0.414;
r(27,28)=0.21;
r(28,29)=0.395;
r(29,30)=0.248;
r(30,31)=0.279;
r(26,32)=0.205;
r(32,33)=0.263;
r(32,34)=0.071;
r(34,35)=0.625;
r(34,36)=0.51;
r(36,37)=2.018;
r(34,38)=1.062;
r(38,39)=0.61;
r(39,40)=2.349;
r(34,41)=0.115;
r(41,42)=0.159;
r(42,43)=0.934;
r(42,44)=0.506;
r(42,45)=0.095;
r(42,46)=1.915;
r(41,47)=0.157;
r(47,48)=1.641;
r(47,49)=0.081;
r(49,50)=1.727;
r(49,51)=0.112;
r(51,52)=0.674;
r(51,53)=0.07;
r(53,54)=2.041;
r(53,55)=0.813;
r(53,56)=0.141;


x(1,2)=0.388;           % x matrix, imply network reactance
x(2,3)=0.315;
x(2,4)=0.349;
x(4,5)=0.421;
x(4,6)=0.466;
x(4,7)=0.468;
x(7,8)=0.314;
x(8,9)=0.798;
x(8,10)=0.441;
x(10,11)=0.327;
x(11,12)=0.999;
x(11,13)=0.377;
x(13,14)=0.257;
x(13,15)=0.401;
x(15,16)=0.385;
x(15,17)=0.134;
x(17,18)=0.722;
x(18,19)=0.721;
x(4,20)=0.334;
x(20,21)=0.096;
x(21,22)=0.695;
x(20,23)=0.542;
x(23,24)=0.028;
x(23,25)=0.687;
x(25,26)=0.414;
x(26,27)=0.386;
x(27,28)=0.196;
x(28,29)=0.369;
x(29,30)=0.232;
x(30,31)=0.26;
x(26,32)=0.495;
x(32,33)=0.073;
x(32,34)=0.171;
x(34,35)=0.273;
x(34,36)=0.209;
x(36,37)=0.829;
x(34,38)=0.406;
x(38,39)=0.238;
x(39,40)=0.964;
x(34,41)=0.278;
x(41,42)=0.384;
x(42,43)=0.383;
x(42,44)=0.163;
x(42,45)=0.195;
x(42,46)=0.769;
x(41,47)=0.379;
x(47,48)=0.67;
x(47,49)=0.196;
x(49,50)=0.709;
x(49,51)=0.27;
x(51,52)=0.275;
x(51,53)=0.17;
x(53,54)=0.78;
x(53,55)=0.334;
x(53,56)=0.34;

% load matrix
pf = 0.9;                   % power factor
pfsin = sqrt(1-pf^2);

sc(1)=-4;
sc(3)=0.057;
sc(5)=0.121;
sc(6)=0.049;
sc(7)=0.053;
sc(8)=0.047;
sc(9)=0.068;
sc(10)=0.048;
sc(11)=0.067;
sc(12)=0.094;
sc(14)=0.057;
sc(16)=0.053;
sc(17)=0.057;
sc(18)=0.112;
sc(19)=0.087;
sc(22)=0.063;
sc(24)=0.135;
sc(25)=0.1;
sc(27)=0.48;
sc(28)=0.38;
sc(29)=0.044;
sc(31)=0.053;
sc(32)=0.223;
sc(33)=0.123;
sc(34)=0.067;
sc(35)=0.094;
sc(36)=0.097;
sc(37)=0.281;
sc(38)=0.117;
sc(39)=0.131;
sc(40)=0.03;
sc(41)=0.046;
sc(42)=0.054;
sc(43)=0.083;
sc(44)=0.057;
sc(46)=0.134;
sc(47)=0.045;
sc(48)=0.196;
sc(50)=0.045;
sc(52)=0.315;
sc(54)=0.061;
sc(55)=0.055;
sc(56)=0.13;

qg_max(45)=5;                   % reactive power upper bound

for i=1:i_total                 % calculate the real and reactive power
    pc(i) = pcs(pc_s)*sc(i)*pf;
    qc(i) = pcs(pc_s)*sc(i)*pfsin;
end

for i=1:i_total
    alpha(i)=pc(i);
end

qg(45)=0;                       % PV reactive power initialization


    pg(45) = pgs_45(pg_i);      % PV real power initialization

Solution

The optimal power flow problem is sovled by CVX optimization toolbox.

i=0;
k=0;

cvx_begin                       % start the optimization tools

variable l(i_total,j_total);    % state all the optimization variables
variable v(i_total,1);
variable s(i_total,1);
variable t(i_total,1);
variable P(i_total,j_total);
variable Q(i_total,j_total);
variable qg(i_total,1);


minimize (trace(r'*l)+alpha'*v+(cv'*s+cr'*t))       % the total minimization objective, eqa(17) in paper page 4

subject to


    s >= norm([pg qg]);                             % s constraint, eqa(22)
    t >= pg.^2+qg.^2;                               % t constraint, eqa(23)
    abs(qg) <= qg_max;                              % PV reactive power constraint, eqa(24)
    4 <= v <= 18;                                   % V upper and down constraint, eqa(25)
    for h=2:i_total
        pc_min <= pc(h);                            % demand power constraint, eqa(26)
        qc_min <= qc(h);
    end

    for i=1:i_total
        for k=i+1:j_total
            P(i,k) == P(k,:)*E(k,:)' + r(i,k)*l(i,k)+ pc(k)-pg(k);                         % P constraint, eqa(18)
            Q(i,k) == Q(k,:)*E(k,:)' + x(i,k)*l(i,k)+ qc(k)-qg(k)-v(k)*qc(k);              % Q constraint, eqa(19)

            v(k)*E(i,k) == (v(i)-2*(r(i,k)*P(i,k)+x(i,k)*Q(i,k))+(r(i,k)^2+x(i,k)^2)*l(i,k))*E(i,k);        % V constraint, eqa(20)
            norm([2*P(i,k); 2*Q(i,k); l(i,k)-v(i)])*E(i,k) <= (l(i,k)+v(i))*E(i,k);                         % lij constraint, eqa(21)
        end
    end


cvx_end                         % end the optimization tools

    qgs_45(pg_i) = qg(45);

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.4e+02|6.8e+09| 7.418049e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.052|0.224|4.0e+02|1.1e+02|1.3e+09| 1.115301e+06 -6.094329e+04| 0:0:01| spchol  1  1 
 2|0.297|0.469|2.8e+02|5.6e+01|3.3e+08| 1.881921e+06 -9.780323e+04| 0:0:02| spchol  1  1 
 3|0.851|0.820|4.2e+01|1.0e+01|4.3e+07| 2.161794e+06 -1.075172e+05| 0:0:02| spchol  1  1 
 4|0.899|0.908|4.2e+00|9.4e-01|4.3e+06| 6.084129e+05 -9.461980e+04| 0:0:03| spchol  1  1 
 5|0.689|0.592|1.3e+00|3.8e-01|1.6e+06| 2.371280e+05 -6.809223e+04| 0:0:03| spchol  1  1 
 6|0.786|0.484|2.8e-01|2.0e-01|4.9e+05| 7.679398e+04 -4.387639e+04| 0:0:04| spchol  1  1 
 7|0.451|0.322|1.5e-01|1.4e-01|3.1e+05| 4.740521e+04 -3.137198e+04| 0:0:04| spchol  1  1 
 8|0.560|0.340|6.7e-02|9.0e-02|1.7e+05| 2.577517e+04 -2.178906e+04| 0:0:04| spchol  1  1 
 9|0.626|0.341|2.5e-02|6.4e-02|1.0e+05| 1.343599e+04 -1.495464e+04| 0:0:05| spchol  1  1 
10|0.576|0.560|1.1e-02|3.2e-02|5.4e+04| 8.274849e+03 -7.083992e+03| 0:0:05| spchol  1  1 
11|0.752|0.336|2.7e-03|2.3e-02|2.9e+04| 4.071788e+03 -4.854818e+03| 0:0:05| spchol  1  1 
12|0.891|0.358|2.9e-04|1.5e-02|1.5e+04| 1.808056e+03 -3.205423e+03| 0:0:06| spchol  1  1 
13|0.804|0.372|5.7e-05|9.4e-03|8.6e+03| 9.245574e+02 -2.069381e+03| 0:0:06| spchol  1  1 
14|0.545|0.337|2.6e-05|6.3e-03|5.7e+03| 5.706692e+02 -1.404269e+03| 0:0:07| spchol  1  1 
15|0.574|0.224|1.1e-05|4.9e-03|4.2e+03| 3.203610e+02 -1.105344e+03| 0:0:07| spchol  1  1 
16|0.601|0.239|4.5e-06|3.7e-03|3.1e+03| 1.724384e+02 -8.549102e+02| 0:0:07| spchol  1  1 
17|0.490|0.242|2.3e-06|2.8e-03|2.4e+03| 1.083377e+02 -6.595438e+02| 0:0:08| spchol  1  1 
18|0.549|0.217|1.1e-06|2.2e-03|1.8e+03| 6.773755e+01 -5.243584e+02| 0:0:08| spchol  1  1 
19|0.610|0.253|4.3e-07|1.6e-03|1.4e+03| 3.884998e+01 -3.990985e+02| 0:0:09| spchol  1  1 
20|0.779|0.274|1.4e-07|1.2e-03|1.0e+03| 1.379776e+01 -2.967340e+02| 0:0:09| spchol  1  1 
21|1.000|0.258|1.1e-07|8.9e-04|7.6e+02|-6.867077e+00 -2.285294e+02| 0:0:09| spchol  1  1 
22|1.000|0.324|8.0e-08|6.0e-04|5.1e+02|-3.576366e+01 -1.721892e+02| 0:0:10| spchol  1  1 
23|1.000|0.416|4.0e-08|3.5e-04|2.9e+02|-5.233241e+01 -1.260449e+02| 0:0:10| spchol  1  1 
24|1.000|0.404|2.0e-08|2.1e-04|1.7e+02|-5.619514e+01 -9.948139e+01| 0:0:11| spchol  1  1 
25|1.000|0.396|1.0e-08|1.3e-04|1.0e+02|-5.766626e+01 -8.372892e+01| 0:0:11| spchol  1  1 
26|1.000|0.326|7.1e-09|8.5e-05|6.9e+01|-5.816835e+01 -7.584037e+01| 0:0:11| spchol  1  1 
27|1.000|0.314|5.1e-09|5.8e-05|4.8e+01|-5.844148e+01 -7.069926e+01| 0:0:12| spchol  1  1 
28|1.000|0.324|3.6e-09|3.9e-05|3.3e+01|-5.862886e+01 -6.701653e+01| 0:0:12| spchol  1  1 
29|1.000|0.314|2.6e-09|2.7e-05|2.3e+01|-5.874571e+01 -6.458233e+01| 0:0:13| spchol  1  1 
30|1.000|0.311|2.0e-09|1.9e-05|1.6e+01|-5.882863e+01 -6.291704e+01| 0:0:13| spchol  1  1 
31|1.000|0.317|1.4e-09|1.3e-05|1.1e+01|-5.889945e+01 -6.173267e+01| 0:0:13| spchol  1  1 
32|1.000|0.340|9.6e-10|8.4e-06|7.4e+00|-5.896344e+01 -6.085594e+01| 0:0:14| spchol  1  1 
33|1.000|0.333|6.4e-10|5.6e-06|5.0e+00|-5.900754e+01 -6.028161e+01| 0:0:14| spchol  1  1 
34|1.000|0.337|4.3e-10|3.7e-06|3.3e+00|-5.903611e+01 -5.988970e+01| 0:0:15| spchol  1  1 
35|1.000|0.366|2.4e-10|2.4e-06|2.1e+00|-5.906053e+01 -5.960333e+01| 0:0:15| spchol  1  1 
36|0.942|0.402|1.4e-10|1.4e-06|1.2e+00|-5.907514e+01 -5.940079e+01| 0:0:15| spchol  1  1 
37|1.000|0.340|7.4e-11|9.3e-07|8.1e-01|-5.908226e+01 -5.929735e+01| 0:0:16| spchol  1  1 
38|1.000|0.350|4.9e-11|6.0e-07|5.3e-01|-5.908561e+01 -5.922640e+01| 0:0:16| spchol  1  1 
39|1.000|0.367|5.5e-11|3.2e-06|3.4e-01|-5.908821e+01 -5.917749e+01| 0:0:17| spchol  1  1 
40|0.953|0.923|1.5e-11|2.1e-06|3.8e-02|-5.908976e+01 -5.909896e+01| 0:0:17| spchol  1  1 
41|0.559|0.944|7.8e-12|2.4e-07|7.9e-03|-5.909058e+01 -5.909205e+01| 0:0:17| spchol  1  1 
42|0.566|0.472|4.0e-12|4.8e-08|4.2e-03|-5.909101e+01 -5.909183e+01| 0:0:18| spchol  1  1 
43|0.567|0.472|2.2e-12|2.6e-08|2.3e-03|-5.909124e+01 -5.909169e+01| 0:0:18| spchol  1  1 
44|0.569|0.472|5.2e-12|1.4e-08|1.2e-03|-5.909136e+01 -5.909161e+01| 0:0:19| spchol  1  1 
45|0.571|0.472|5.7e-12|7.4e-09|6.5e-04|-5.909142e+01 -5.909156e+01| 0:0:19| spchol  1  1 
46|0.573|0.472|6.2e-12|4.0e-09|3.5e-04|-5.909145e+01 -5.909153e+01| 0:0:19| spchol  1  1 
47|0.575|0.472|7.6e-12|2.1e-09|1.9e-04|-5.909147e+01 -5.909151e+01| 0:0:20| spchol  1  1 
48|0.577|0.471|5.3e-13|1.2e-09|1.0e-04|-5.909148e+01 -5.909151e+01| 0:0:20| spchol  1  1 
49|0.582|0.471|8.3e-12|6.3e-10|5.7e-05|-5.909149e+01 -5.909150e+01| 0:0:21| spchol  1  1 
50|0.586|0.471|1.3e-11|3.5e-10|3.3e-05|-5.909149e+01 -5.909150e+01| 0:0:21| spchol  1  1 
51|0.598|0.471|1.2e-11|2.0e-10|1.9e-05|-5.909149e+01 -5.909149e+01| 0:0:21| spchol  1  1 
52|0.617|0.471|2.9e-12|1.2e-10|1.1e-05|-5.909149e+01 -5.909149e+01| 0:0:22| spchol  1  1 
53|0.641|0.471|3.4e-12|7.0e-11|6.8e-06|-5.909149e+01 -5.909149e+01| 0:0:22| spchol  1  1 
54|0.670|0.471|2.9e-12|4.1e-11|4.0e-06|-5.909149e+01 -5.909149e+01| 0:0:23| spchol  1  1 
55|0.705|0.471|5.0e-13|2.5e-11|2.4e-06|-5.909149e+01 -5.909149e+01| 0:0:23| spchol  1  1 
56|0.749|0.471|3.1e-12|1.5e-11|1.4e-06|-5.909149e+01 -5.909149e+01| 0:0:24|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 56
 primal objective value = -5.90914926e+01
 dual   objective value = -5.90914928e+01
 gap := trace(XZ)       = 1.40e-06
 relative gap           = 1.17e-08
 actual relative gap    = 1.75e-09
 rel. primal infeas (scaled problem)   = 3.13e-12
 rel. dual     "        "       "      = 1.45e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.5e+04, 1.3e+07, 1.3e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 23.53  
 CPU time per iteration = 0.42  
 termination code       =  0
 DIMACS: 3.2e-12  0.0e+00  1.5e-10  0.0e+00  1.8e-09  1.2e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +51.0106
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.424049e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.053|0.226|4.0e+02|1.0e+02|1.3e+09| 1.117618e+06 -6.094845e+04| 0:0:01| spchol  1  1 
 2|0.302|0.472|2.8e+02|5.5e+01|3.2e+08| 1.898885e+06 -9.802257e+04| 0:0:01| spchol  1  1 
 3|0.852|0.819|4.1e+01|1.0e+01|4.3e+07| 2.170795e+06 -1.077735e+05| 0:0:01| spchol  1  1 
 4|0.907|0.908|3.8e+00|9.2e-01|4.0e+06| 5.960884e+05 -9.456689e+04| 0:0:02| spchol  1  1 
 5|0.691|0.596|1.2e+00|3.8e-01|1.5e+06| 2.289674e+05 -6.620637e+04| 0:0:02| spchol  1  1 
 6|0.781|0.480|2.6e-01|2.0e-01|4.7e+05| 7.460676e+04 -4.234660e+04| 0:0:03| spchol  1  1 
 7|0.445|0.312|1.4e-01|1.4e-01|3.0e+05| 4.652196e+04 -3.062375e+04| 0:0:03| spchol  1  1 
 8|0.559|0.344|6.3e-02|8.9e-02|1.7e+05| 2.545665e+04 -2.114390e+04| 0:0:03| spchol  1  1 
 9|0.599|0.339|2.5e-02|6.4e-02|1.0e+05| 1.385774e+04 -1.456340e+04| 0:0:04| spchol  1  1 
10|0.559|0.558|1.1e-02|3.2e-02|5.4e+04| 8.662537e+03 -6.940114e+03| 0:0:04| spchol  1  1 
11|0.734|0.298|2.9e-03|2.4e-02|3.1e+04| 4.314159e+03 -5.013545e+03| 0:0:05| spchol  1  1 
12|0.866|0.394|4.0e-04|1.5e-02|1.5e+04| 1.931332e+03 -3.135176e+03| 0:0:05| spchol  1  1 
13|0.827|0.367|6.9e-05|9.6e-03|8.6e+03| 9.210057e+02 -2.043039e+03| 0:0:05| spchol  1  1 
14|0.468|0.328|3.7e-05|6.5e-03|5.8e+03| 6.123420e+02 -1.404100e+03| 0:0:06| spchol  1  1 
15|0.572|0.212|1.6e-05|5.1e-03|4.3e+03| 3.372764e+02 -1.121976e+03| 0:0:06| spchol  1  1 
16|0.731|0.232|4.3e-06|3.9e-03|3.2e+03| 1.443767e+02 -8.764530e+02| 0:0:06| spchol  1  1 
17|0.457|0.283|2.3e-06|2.8e-03|2.3e+03| 9.949187e+01 -6.426247e+02| 0:0:07| spchol  1  1 
18|0.537|0.216|1.1e-06|2.2e-03|1.8e+03| 6.252582e+01 -5.129986e+02| 0:0:07| spchol  1  1 
19|0.608|0.247|4.5e-07|1.7e-03|1.4e+03| 2.955450e+01 -3.962088e+02| 0:0:08| spchol  1  1 
20|0.755|0.246|1.6e-07|1.3e-03|1.0e+03|-7.888237e+00 -3.126238e+02| 0:0:08| spchol  1  1 
21|1.000|0.282|9.6e-08|9.0e-04|7.2e+02|-5.942659e+01 -2.483871e+02| 0:0:08| spchol  1  1 
22|1.000|0.396|5.5e-08|5.4e-04|4.4e+02|-7.665800e+01 -1.856575e+02| 0:0:09| spchol  1  1 
23|1.000|0.374|3.4e-08|3.4e-04|2.7e+02|-8.162162e+01 -1.494702e+02| 0:0:09| spchol  1  1 
24|1.000|0.391|1.8e-08|2.1e-04|1.7e+02|-8.413864e+01 -1.253571e+02| 0:0:09| spchol  1  1 
25|1.000|0.367|1.0e-08|1.3e-04|1.0e+02|-8.524934e+01 -1.114138e+02| 0:0:09| spchol  1  1 
26|1.000|0.319|7.4e-09|8.9e-05|7.2e+01|-8.570476e+01 -1.036901e+02| 0:0:10| spchol  1  1 
27|1.000|0.314|5.4e-09|6.1e-05|5.0e+01|-8.597932e+01 -9.846421e+01| 0:0:10| spchol  1  1 
28|1.000|0.323|3.8e-09|4.2e-05|3.4e+01|-8.617796e+01 -9.473608e+01| 0:0:10| spchol  1  1 
29|1.000|0.316|2.8e-09|2.8e-05|2.4e+01|-8.630557e+01 -9.224833e+01| 0:0:11| spchol  1  1 
30|1.000|0.312|2.1e-09|2.0e-05|1.7e+01|-8.639554e+01 -9.054707e+01| 0:0:11| spchol  1  1 
31|1.000|0.320|1.5e-09|1.3e-05|1.1e+01|-8.647157e+01 -8.933755e+01| 0:0:11| spchol  1  1 
32|1.000|0.341|9.7e-10|8.8e-06|7.6e+00|-8.653873e+01 -8.844799e+01| 0:0:11| spchol  1  1 
33|1.000|0.330|6.5e-10|5.9e-06|5.1e+00|-8.658236e+01 -8.787422e+01| 0:0:12| spchol  1  1 
34|1.000|0.329|4.6e-10|3.9e-06|3.5e+00|-8.660957e+01 -8.748774e+01| 0:0:12| spchol  1  1 
35|1.000|0.356|2.7e-10|2.5e-06|2.2e+00|-8.663380e+01 -8.720288e+01| 0:0:12| spchol  1  1 
36|0.990|0.390|1.5e-10|1.5e-06|1.3e+00|-8.665029e+01 -8.699826e+01| 0:0:12| spchol  1  1 
37|0.992|0.375|7.9e-11|9.7e-07|8.4e-01|-8.665888e+01 -8.687658e+01| 0:0:13| spchol  1  1 
38|1.000|0.360|7.7e-11|6.2e-07|5.3e-01|-8.666289e+01 -8.680283e+01| 0:0:13| spchol  1  1 
39|1.000|0.310|4.3e-11|3.2e-06|3.8e-01|-8.666450e+01 -8.676201e+01| 0:0:13| spchol  1  1 
40|1.000|0.903|2.7e-11|2.3e-06|5.8e-02|-8.666566e+01 -8.667929e+01| 0:0:14| spchol  1  1 
41|0.593|0.941|1.3e-11|3.5e-07|1.4e-02|-8.666709e+01 -8.666963e+01| 0:0:14| spchol  1  1 
42|0.563|0.472|7.0e-12|8.2e-08|7.2e-03|-8.666785e+01 -8.666926e+01| 0:0:14| spchol  1  1 
43|0.564|0.472|4.6e-12|4.4e-08|3.9e-03|-8.666824e+01 -8.666903e+01| 0:0:15| spchol  1  1 
44|0.566|0.472|2.3e-12|2.3e-08|2.1e-03|-8.666846e+01 -8.666889e+01| 0:0:15| spchol  1  1 
45|0.568|0.472|3.2e-12|1.3e-08|1.1e-03|-8.666857e+01 -8.666881e+01| 0:0:15| spchol  1  1 
46|0.570|0.472|1.4e-11|6.8e-09|6.0e-04|-8.666863e+01 -8.666876e+01| 0:0:16| spchol  1  1 
47|0.571|0.472|1.0e-11|3.6e-09|3.2e-04|-8.666866e+01 -8.666873e+01| 0:0:16| spchol  1  1 
48|0.574|0.471|2.7e-11|2.0e-09|1.8e-04|-8.666867e+01 -8.666871e+01| 0:0:16| spchol  1  1 
49|0.577|0.471|3.4e-12|1.1e-09|9.8e-05|-8.666868e+01 -8.666871e+01| 0:0:17| spchol  1  1 
50|0.585|0.471|1.2e-12|6.0e-10|5.4e-05|-8.666869e+01 -8.666870e+01| 0:0:17| spchol  1  1 
51|0.590|0.471|1.6e-12|3.3e-10|3.1e-05|-8.666869e+01 -8.666870e+01| 0:0:18| spchol  1  1 
52|0.600|0.471|2.7e-12|1.9e-10|1.8e-05|-8.666869e+01 -8.666870e+01| 0:0:18| spchol  1  1 
53|0.618|0.471|8.4e-12|1.1e-10|1.1e-05|-8.666869e+01 -8.666869e+01| 0:0:19| spchol  1  1 
54|0.642|0.471|1.3e-12|6.5e-11|6.3e-06|-8.666869e+01 -8.666869e+01| 0:0:19| spchol  1  1 
55|0.670|0.471|1.8e-12|3.8e-11|3.7e-06|-8.666869e+01 -8.666869e+01| 0:0:20| spchol  1  1 
56|0.706|0.471|9.1e-13|2.3e-11|2.2e-06|-8.666869e+01 -8.666869e+01| 0:0:21|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 56
 primal objective value = -8.66686928e+01
 dual   objective value = -8.66686931e+01
 gap := trace(XZ)       = 2.19e-06
 relative gap           = 1.26e-08
 actual relative gap    = 2.01e-09
 rel. primal infeas (scaled problem)   = 9.06e-13
 rel. dual     "        "       "      = 2.26e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.6e+04, 1.3e+07, 1.3e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 20.59  
 CPU time per iteration = 0.37  
 termination code       =  0
 DIMACS: 9.2e-13  0.0e+00  2.1e-10  0.0e+00  2.0e-09  1.3e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +80.3378
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.430049e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.054|0.229|4.0e+02|1.0e+02|1.3e+09| 1.120567e+06 -6.101109e+04| 0:0:01| spchol  1  1 
 2|0.311|0.477|2.7e+02|5.4e+01|3.2e+08| 1.922426e+06 -9.838072e+04| 0:0:02| spchol  1  1 
 3|0.855|0.818|3.9e+01|9.8e+00|4.2e+07| 2.182605e+06 -1.081773e+05| 0:0:03| spchol  1  1 
 4|0.915|0.909|3.3e+00|9.0e-01|3.7e+06| 5.824389e+05 -9.453262e+04| 0:0:03| spchol  1  1 
 5|0.696|0.603|1.0e+00|3.6e-01|1.3e+06| 2.188059e+05 -6.389915e+04| 0:0:04| spchol  1  1 
 6|0.776|0.474|2.3e-01|1.9e-01|4.4e+05| 7.174473e+04 -4.055164e+04| 0:0:04| spchol  1  1 
 7|0.434|0.298|1.3e-01|1.3e-01|2.8e+05| 4.546848e+04 -2.978292e+04| 0:0:05| spchol  1  1 
 8|0.560|0.344|5.7e-02|8.8e-02|1.6e+05| 2.494165e+04 -2.055122e+04| 0:0:06| spchol  1  1 
 9|0.576|0.359|2.4e-02|6.2e-02|9.8e+04| 1.405893e+04 -1.376775e+04| 0:0:06| spchol  1  1 
10|0.543|0.519|1.1e-02|3.3e-02|5.5e+04| 8.895406e+03 -7.081608e+03| 0:0:07| spchol  1  1 
11|0.746|0.287|2.8e-03|2.5e-02|3.1e+04| 4.359905e+03 -5.188593e+03| 0:0:08| spchol  1  1 
12|0.853|0.409|4.1e-04|1.5e-02|1.5e+04| 1.982449e+03 -3.168126e+03| 0:0:08| spchol  1  1 
13|0.872|0.376|5.3e-05|9.7e-03|8.4e+03| 8.765482e+02 -2.038452e+03| 0:0:09| spchol  1  1 
14|0.433|0.334|3.0e-05|6.5e-03|5.7e+03| 6.020538e+02 -1.390541e+03| 0:0:10| spchol  1  1 
15|0.576|0.204|1.3e-05|5.2e-03|4.3e+03| 3.251366e+02 -1.121155e+03| 0:0:10| spchol  1  1 
16|0.720|0.231|3.6e-06|4.0e-03|3.1e+03| 1.387620e+02 -8.768839e+02| 0:0:11| spchol  1  1 
17|0.445|0.277|2.0e-06|2.9e-03|2.3e+03| 9.600014e+01 -6.498523e+02| 0:0:11| spchol  1  1 
18|0.554|0.212|9.3e-07|2.3e-03|1.8e+03| 5.248511e+01 -5.244085e+02| 0:0:12| spchol  1  1 
19|0.619|0.253|3.7e-07|1.7e-03|1.3e+03| 4.860360e+00 -4.103752e+02| 0:0:12| spchol  1  1 
20|0.791|0.259|1.3e-07|1.3e-03|9.7e+02|-5.988897e+01 -3.331578e+02| 0:0:13| spchol  1  1 
21|1.000|0.331|7.4e-08|8.4e-04|6.4e+02|-9.905625e+01 -2.623808e+02| 0:0:14| spchol  1  1 
22|1.000|0.364|5.0e-08|5.4e-04|4.2e+02|-1.057783e+02 -2.095900e+02| 0:0:14| spchol  1  1 
23|1.000|0.369|3.1e-08|3.4e-04|2.6e+02|-1.096743e+02 -1.751536e+02| 0:0:15| spchol  1  1 
24|1.000|0.387|1.6e-08|2.1e-04|1.6e+02|-1.119098e+02 -1.519786e+02| 0:0:16| spchol  1  1 
25|1.000|0.349|1.0e-08|1.3e-04|1.0e+02|-1.128404e+02 -1.390510e+02| 0:0:16| spchol  1  1 
26|1.000|0.310|7.6e-09|9.3e-05|7.3e+01|-1.132391e+02 -1.315326e+02| 0:0:17| spchol  1  1 
27|1.000|0.307|5.7e-09|6.4e-05|5.1e+01|-1.135037e+02 -1.263503e+02| 0:0:17| spchol  1  1 
28|1.000|0.322|4.1e-09|4.4e-05|3.5e+01|-1.137199e+02 -1.225542e+02| 0:0:18| spchol  1  1 
29|1.000|0.324|2.9e-09|3.0e-05|2.4e+01|-1.138749e+02 -1.199358e+02| 0:0:19| spchol  1  1 
30|1.000|0.321|2.0e-09|2.0e-05|1.7e+01|-1.139839e+02 -1.181570e+02| 0:0:19| spchol  1  1 
31|1.000|0.326|1.4e-09|1.3e-05|1.1e+01|-1.140674e+02 -1.169166e+02| 0:0:20| spchol  1  1 
32|1.000|0.345|9.1e-10|8.8e-06|7.4e+00|-1.141362e+02 -1.160201e+02| 0:0:20| spchol  1  1 
33|1.000|0.326|6.2e-10|6.0e-06|5.0e+00|-1.141765e+02 -1.154611e+02| 0:0:21| spchol  1  1 
34|1.000|0.317|4.6e-10|4.1e-06|3.5e+00|-1.141998e+02 -1.150906e+02| 0:0:22| spchol  1  1 
35|1.000|0.332|3.1e-10|2.7e-06|2.4e+00|-1.142207e+02 -1.148229e+02| 0:0:22| spchol  1  1 
36|1.000|0.374|1.9e-10|1.7e-06|1.5e+00|-1.142386e+02 -1.146178e+02| 0:0:23| spchol  1  1 
37|0.890|0.406|1.1e-10|1.0e-06|8.7e-01|-1.142493e+02 -1.144756e+02| 0:0:24| spchol  1  1 
38|0.933|0.355|5.2e-11|6.5e-07|5.5e-01|-1.142551e+02 -1.144008e+02| 0:0:24| spchol  1  1 
39|0.990|0.354|3.4e-11|3.3e-06|3.6e-01|-1.142581e+02 -1.143522e+02| 0:0:25| spchol  1  1 
40|0.996|0.925|1.8e-11|2.2e-06|4.0e-02|-1.142598e+02 -1.142693e+02| 0:0:25| spchol  1  1 
41|0.559|0.943|9.4e-12|2.4e-07|8.2e-03|-1.142606e+02 -1.142622e+02| 0:0:26| spchol  1  1 
42|0.565|0.472|4.7e-12|5.0e-08|4.4e-03|-1.142611e+02 -1.142619e+02| 0:0:27| spchol  1  1 
43|0.567|0.472|2.3e-12|2.6e-08|2.3e-03|-1.142613e+02 -1.142618e+02| 0:0:27| spchol  1  1 
44|0.569|0.472|1.9e-12|1.4e-08|1.3e-03|-1.142614e+02 -1.142617e+02| 0:0:28| spchol  1  1 
45|0.570|0.472|1.0e-11|7.6e-09|6.8e-04|-1.142615e+02 -1.142616e+02| 0:0:29| spchol  1  1 
46|0.572|0.472|1.2e-11|4.1e-09|3.6e-04|-1.142615e+02 -1.142616e+02| 0:0:29| spchol  1  1 
47|0.575|0.472|5.8e-12|2.2e-09|2.0e-04|-1.142616e+02 -1.142616e+02| 0:0:30| spchol  1  1 
48|0.578|0.471|7.9e-12|1.2e-09|1.1e-04|-1.142616e+02 -1.142616e+02| 0:0:30| spchol  1  1 
49|0.582|0.471|4.2e-12|6.5e-10|6.0e-05|-1.142616e+02 -1.142616e+02| 0:0:31| spchol  1  1 
50|0.585|0.471|1.2e-11|3.6e-10|3.4e-05|-1.142616e+02 -1.142616e+02| 0:0:32| spchol  1  1 
51|0.594|0.471|1.2e-11|2.0e-10|2.0e-05|-1.142616e+02 -1.142616e+02| 0:0:32| spchol  1  1 
52|0.613|0.471|5.1e-12|1.2e-10|1.2e-05|-1.142616e+02 -1.142616e+02| 0:0:33| spchol  1  1 
53|0.636|0.471|4.5e-12|7.1e-11|7.0e-06|-1.142616e+02 -1.142616e+02| 0:0:34| spchol  1  1 
54|0.663|0.471|4.4e-12|4.2e-11|4.1e-06|-1.142616e+02 -1.142616e+02| 0:0:34| spchol  1  1 
55|0.697|0.471|5.3e-12|2.5e-11|2.4e-06|-1.142616e+02 -1.142616e+02| 0:0:35|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 55
 primal objective value = -1.14261579e+02
 dual   objective value = -1.14261579e+02
 gap := trace(XZ)       = 2.44e-06
 relative gap           = 1.06e-08
 actual relative gap    = 1.69e-09
 rel. primal infeas (scaled problem)   = 5.27e-12
 rel. dual     "        "       "      = 2.53e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.3e+04, 1.3e+07, 1.3e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 34.77  
 CPU time per iteration = 0.63  
 termination code       =  0
 DIMACS: 5.3e-12  0.0e+00  1.9e-10  0.0e+00  1.7e-09  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +110.181
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.436049e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.055|0.231|3.9e+02|1.0e+02|1.3e+09| 1.124109e+06 -6.113962e+04| 0:0:01| spchol  1  1 
 2|0.322|0.482|2.7e+02|5.3e+01|3.2e+08| 1.952877e+06 -9.886989e+04| 0:0:02| spchol  1  1 
 3|0.860|0.819|3.7e+01|9.6e+00|4.0e+07| 2.181992e+06 -1.084019e+05| 0:0:03| spchol  1  1 
 4|0.921|0.908|2.9e+00|8.8e-01|3.4e+06| 5.628607e+05 -9.412762e+04| 0:0:03| spchol  1  1 
 5|0.709|0.619|8.6e-01|3.4e-01|1.2e+06| 2.030257e+05 -6.080784e+04| 0:0:04| spchol  1  1 
 6|0.771|0.469|2.0e-01|1.8e-01|4.0e+05| 6.689945e+04 -3.816672e+04| 0:0:04| spchol  1  1 
 7|0.423|0.290|1.1e-01|1.3e-01|2.6e+05| 4.304735e+04 -2.828713e+04| 0:0:05| spchol  1  1 
 8|0.606|0.353|4.5e-02|8.3e-02|1.4e+05| 2.214543e+04 -1.921047e+04| 0:0:06| spchol  1  1 
 9|0.512|0.473|2.2e-02|4.9e-02|8.4e+04| 1.367097e+04 -1.077490e+04| 0:0:06| spchol  1  1 
10|0.529|0.363|1.0e-02|3.4e-02|5.4e+04| 8.545561e+03 -7.134287e+03| 0:0:07| spchol  1  1 
11|0.774|0.338|2.3e-03|2.4e-02|2.8e+04| 4.033496e+03 -4.876992e+03| 0:0:08| spchol  1  1 
12|0.860|0.378|3.2e-04|1.5e-02|1.4e+04| 1.793138e+03 -3.120184e+03| 0:0:09| spchol  1  1 
13|0.862|0.374|4.5e-05|9.7e-03|8.0e+03| 7.999559e+02 -2.011092e+03| 0:0:09| spchol  1  1 
14|0.448|0.328|2.5e-05|6.5e-03|5.5e+03| 5.401947e+02 -1.382110e+03| 0:0:10| spchol  1  1 
15|0.604|0.208|9.8e-06|5.2e-03|4.1e+03| 2.780600e+02 -1.109615e+03| 0:0:10| spchol  1  1 
16|0.469|0.244|5.3e-06|3.9e-03|3.1e+03| 1.733585e+02 -8.551669e+02| 0:0:11| spchol  1  1 
17|0.512|0.200|2.6e-06|3.1e-03|2.5e+03| 9.846947e+01 -6.976744e+02| 0:0:12| spchol  1  1 
18|0.525|0.216|1.2e-06|2.5e-03|1.9e+03| 4.217314e+01 -5.656901e+02| 0:0:12| spchol  1  1 
19|0.570|0.235|5.5e-07|1.9e-03|1.4e+03|-2.010631e+01 -4.619134e+02| 0:0:13| spchol  1  1 
20|0.732|0.277|1.8e-07|1.4e-03|1.0e+03|-8.863054e+01 -3.750353e+02| 0:0:13| spchol  1  1 
21|1.000|0.296|7.8e-08|9.6e-04|7.0e+02|-1.262633e+02 -3.078222e+02| 0:0:14| spchol  1  1 
22|1.000|0.363|5.4e-08|6.1e-04|4.6e+02|-1.323316e+02 -2.488809e+02| 0:0:15| spchol  1  1 
23|1.000|0.365|3.5e-08|3.9e-04|2.9e+02|-1.366092e+02 -2.107177e+02| 0:0:15| spchol  1  1 
24|1.000|0.379|1.9e-08|2.4e-04|1.8e+02|-1.391018e+02 -1.850880e+02| 0:0:16| spchol  1  1 
25|1.000|0.378|1.1e-08|1.5e-04|1.1e+02|-1.403949e+02 -1.690144e+02| 0:0:16| spchol  1  1 
26|1.000|0.296|8.4e-09|1.1e-04|8.0e+01|-1.407569e+02 -1.611613e+02| 0:0:17| spchol  1  1 
27|1.000|0.293|6.9e-09|7.4e-05|5.8e+01|-1.409867e+02 -1.556525e+02| 0:0:18| spchol  1  1 
28|1.000|0.310|5.2e-09|5.1e-05|4.1e+01|-1.412169e+02 -1.515047e+02| 0:0:18| spchol  1  1 
29|1.000|0.323|3.7e-09|3.5e-05|2.8e+01|-1.414161e+02 -1.484926e+02| 0:0:19| spchol  1  1 
30|1.000|0.327|2.6e-09|2.3e-05|1.9e+01|-1.415704e+02 -1.463965e+02| 0:0:20| spchol  1  1 
31|1.000|0.332|1.7e-09|1.6e-05|1.3e+01|-1.416830e+02 -1.449482e+02| 0:0:20| spchol  1  1 
32|1.000|0.346|1.1e-09|1.0e-05|8.4e+00|-1.417704e+02 -1.439248e+02| 0:0:21| spchol  1  1 
33|1.000|0.372|6.1e-10|6.4e-06|5.2e+00|-1.418368e+02 -1.431943e+02| 0:0:22| spchol  1  1 
34|0.906|0.408|3.2e-10|3.8e-06|3.1e+00|-1.418752e+02 -1.426819e+02| 0:0:22| spchol  1  1 
35|1.000|0.251|2.6e-10|2.8e-06|2.3e+00|-1.418839e+02 -1.424946e+02| 0:0:23| spchol  1  1 
36|1.000|0.324|1.9e-10|1.9e-06|1.6e+00|-1.418929e+02 -1.423125e+02| 0:0:24| spchol  1  1 
37|1.000|0.351|1.2e-10|1.2e-06|1.0e+00|-1.419026e+02 -1.421773e+02| 0:0:24| spchol  1  1 
38|1.000|0.383|6.9e-11|7.7e-07|6.4e-01|-1.419097e+02 -1.420798e+02| 0:0:25| spchol  1  1 
39|0.922|0.396|6.0e-11|3.8e-06|3.9e-01|-1.419137e+02 -1.420167e+02| 0:0:25| spchol  1  1 
40|0.883|0.917|1.9e-11|2.3e-06|4.9e-02|-1.419158e+02 -1.419274e+02| 0:0:26| spchol  1  1 
41|0.562|0.943|1.0e-11|2.9e-07|1.1e-02|-1.419169e+02 -1.419189e+02| 0:0:27| spchol  1  1 
42|0.563|0.472|6.2e-12|6.3e-08|5.6e-03|-1.419175e+02 -1.419186e+02| 0:0:27| spchol  1  1 
43|0.565|0.472|1.1e-10|3.4e-08|3.0e-03|-1.419178e+02 -1.419184e+02| 0:0:28| spchol  1  1 
44|0.567|0.472|3.6e-10|1.8e-08|1.6e-03|-1.419180e+02 -1.419183e+02| 0:0:29| spchol  1  1 
45|0.568|0.472|4.3e-10|9.7e-09|8.8e-04|-1.419181e+02 -1.419182e+02| 0:0:29| spchol  1  1 
46|0.570|0.472|1.5e-10|5.2e-09|4.7e-04|-1.419181e+02 -1.419182e+02| 0:0:30| spchol  1  1 
47|0.573|0.472|3.6e-10|2.8e-09|2.6e-04|-1.419181e+02 -1.419182e+02| 0:0:31| spchol  1  1 
48|0.579|0.471|2.4e-10|1.6e-09|1.5e-04|-1.419181e+02 -1.419182e+02| 0:0:31| spchol  1  1 
49|0.592|0.471|7.5e-10|9.1e-10|9.0e-05|-1.419181e+02 -1.419182e+02| 0:0:32| spchol  1  1 
50|0.611|0.471|2.7e-10|5.4e-10|5.3e-05|-1.419182e+02 -1.419182e+02| 0:0:33| spchol  1  1 
51|0.629|0.471|7.7e-11|3.2e-10|3.2e-05|-1.419182e+02 -1.419182e+02| 0:0:33| spchol  1  1 
52|0.656|0.471|1.7e-10|1.9e-10|1.9e-05|-1.419182e+02 -1.419182e+02| 0:0:34| spchol  1  1 
53|0.688|0.471|1.9e-10|1.1e-10|1.1e-05|-1.419182e+02 -1.419182e+02| 0:0:34| spchol  1  1 
54|0.727|0.471|7.0e-11|6.6e-11|6.5e-06|-1.419182e+02 -1.419182e+02| 0:0:35| spchol  1  1 
55|0.777|0.471|3.7e-11|3.9e-11|3.9e-06|-1.419182e+02 -1.419182e+02| 0:0:36|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 55
 primal objective value = -1.41918154e+02
 dual   objective value = -1.41918155e+02
 gap := trace(XZ)       = 3.87e-06
 relative gap           = 1.36e-08
 actual relative gap    = 1.86e-09
 rel. primal infeas (scaled problem)   = 3.67e-11
 rel. dual     "        "       "      = 3.90e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.1e+04, 1.3e+07, 1.3e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 35.75  
 CPU time per iteration = 0.65  
 termination code       =  0
 DIMACS: 3.7e-11  0.0e+00  2.5e-10  0.0e+00  1.9e-09  1.4e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +140.587
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.442049e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.057|0.235|3.9e+02|1.0e+02|1.2e+09| 1.128169e+06 -6.131535e+04| 0:0:01| spchol  1  1 
 2|0.335|0.488|2.6e+02|5.1e+01|3.1e+08| 1.990988e+06 -9.945306e+04| 0:0:02| spchol  1  1 
 3|0.866|0.821|3.5e+01|9.2e+00|3.8e+07| 2.176532e+06 -1.085817e+05| 0:0:02| spchol  1  1 
 4|0.925|0.908|2.6e+00|8.5e-01|3.2e+06| 5.424888e+05 -9.345178e+04| 0:0:03| spchol  1  1 
 5|0.721|0.642|7.3e-01|3.1e-01|1.1e+06| 1.889981e+05 -5.741061e+04| 0:0:04| spchol  1  1 
 6|0.747|0.435|1.9e-01|1.8e-01|3.8e+05| 6.546313e+04 -3.723632e+04| 0:0:04| spchol  1  1 
 7|0.466|0.312|9.9e-02|1.2e-01|2.4e+05| 3.994375e+04 -2.685635e+04| 0:0:05| spchol  1  1 
 8|0.643|0.412|3.5e-02|7.1e-02|1.2e+05| 1.953522e+04 -1.673703e+04| 0:0:05| spchol  1  1 
 9|0.422|0.445|2.0e-02|4.4e-02|7.9e+04| 1.338673e+04 -9.816598e+03| 0:0:06| spchol  1  1 
10|0.634|0.406|7.5e-03|2.9e-02|4.4e+04| 7.237803e+03 -6.094806e+03| 0:0:07| spchol  1  1 
11|0.776|0.309|1.7e-03|2.1e-02|2.3e+04| 3.369706e+03 -4.326884e+03| 0:0:07| spchol  1  1 
12|0.894|0.370|1.8e-04|1.4e-02|1.2e+04| 1.398311e+03 -2.805376e+03| 0:0:08| spchol  1  1 
13|0.776|0.366|4.0e-05|8.8e-03|7.1e+03| 6.774110e+02 -1.826918e+03| 0:0:09| spchol  1  1 
14|0.416|0.309|2.3e-05|6.1e-03|5.0e+03| 4.649760e+02 -1.290501e+03| 0:0:09| spchol  1  1 
15|0.644|0.205|8.4e-06|4.8e-03|3.7e+03| 2.188387e+02 -1.042486e+03| 0:0:10| spchol  1  1 
16|0.491|0.251|4.3e-06|3.6e-03|2.8e+03| 1.279530e+02 -8.009604e+02| 0:0:11| spchol  1  1 
17|0.510|0.223|2.1e-06|2.8e-03|2.2e+03| 5.627331e+01 -6.458019e+02| 0:0:11| spchol  1  1 
18|0.552|0.212|9.8e-07|2.2e-03|1.7e+03|-2.111753e+01 -5.419155e+02| 0:0:12| spchol  1  1 
19|0.624|0.291|3.8e-07|1.6e-03|1.2e+03|-9.242087e+01 -4.363700e+02| 0:0:12| spchol  1  1 
20|0.807|0.279|1.1e-07|1.1e-03|8.2e+02|-1.402990e+02 -3.644009e+02| 0:0:13| spchol  1  1 
21|1.000|0.317|7.1e-08|7.8e-04|5.6e+02|-1.573331e+02 -3.041640e+02| 0:0:14| spchol  1  1 
22|1.000|0.360|4.6e-08|5.0e-04|3.7e+02|-1.623327e+02 -2.567315e+02| 0:0:14| spchol  1  1 
23|1.000|0.378|2.8e-08|3.1e-04|2.3e+02|-1.656645e+02 -2.244897e+02| 0:0:15| spchol  1  1 
24|1.000|0.353|1.7e-08|2.0e-04|1.5e+02|-1.672937e+02 -2.055111e+02| 0:0:15| spchol  1  1 
25|1.000|0.358|1.1e-08|1.3e-04|9.6e+01|-1.682264e+02 -1.929082e+02| 0:0:16| spchol  1  1 
26|1.000|0.332|7.1e-09|8.6e-05|6.4e+01|-1.687063e+02 -1.853316e+02| 0:0:17| spchol  1  1 
27|1.000|0.297|5.7e-09|6.0e-05|4.6e+01|-1.689027e+02 -1.807720e+02| 0:0:17| spchol  1  1 
28|1.000|0.300|4.5e-09|4.2e-05|3.3e+01|-1.690593e+02 -1.775126e+02| 0:0:18| spchol  1  1 
29|1.000|0.314|3.4e-09|2.9e-05|2.3e+01|-1.692005e+02 -1.751086e+02| 0:0:18| spchol  1  1 
30|1.000|0.320|2.4e-09|2.0e-05|1.6e+01|-1.693262e+02 -1.734081e+02| 0:0:19| spchol  1  1 
31|1.000|0.338|1.6e-09|1.3e-05|1.1e+01|-1.694310e+02 -1.721678e+02| 0:0:20| spchol  1  1 
32|1.000|0.357|9.6e-10|8.4e-06|6.8e+00|-1.695137e+02 -1.712860e+02| 0:0:20| spchol  1  1 
33|0.985|0.389|5.2e-10|5.1e-06|4.1e+00|-1.695702e+02 -1.706559e+02| 0:0:21| spchol  1  1 
34|0.895|0.397|2.7e-10|3.1e-06|2.5e+00|-1.696001e+02 -1.702559e+02| 0:0:21| spchol  1  1 
35|1.000|0.337|1.5e-10|2.1e-06|1.6e+00|-1.696156e+02 -1.700491e+02| 0:0:22| spchol  1  1 
36|1.000|0.280|1.2e-10|1.5e-06|1.2e+00|-1.696184e+02 -1.699352e+02| 0:0:23| spchol  1  1 
37|1.000|0.303|1.1e-10|1.0e-06|8.5e-01|-1.696214e+02 -1.698458e+02| 0:0:23| spchol  1  1 
38|1.000|0.316|9.8e-11|7.0e-07|5.9e-01|-1.696247e+02 -1.697803e+02| 0:0:24| spchol  1  1 
39|1.000|0.335|6.7e-11|3.3e-06|4.0e-01|-1.696275e+02 -1.697322e+02| 0:0:25| spchol  1  1 
40|1.000|0.885|3.2e-11|2.4e-06|7.1e-02|-1.696297e+02 -1.696467e+02| 0:0:25| spchol  1  1 
41|0.604|0.942|1.7e-11|4.2e-07|1.7e-02|-1.696315e+02 -1.696347e+02| 0:0:26| spchol  1  1 
42|0.562|0.472|9.0e-12|1.0e-07|9.0e-03|-1.696324e+02 -1.696342e+02| 0:0:26| spchol  1  1 
43|0.563|0.472|4.7e-12|5.3e-08|4.9e-03|-1.696329e+02 -1.696339e+02| 0:0:27| spchol  1  1 
44|0.565|0.472|8.5e-12|2.9e-08|2.6e-03|-1.696332e+02 -1.696337e+02| 0:0:28| spchol  1  1 
45|0.567|0.472|2.9e-12|1.5e-08|1.4e-03|-1.696333e+02 -1.696336e+02| 0:0:28| spchol  1  1 
46|0.569|0.472|5.7e-12|8.2e-09|7.5e-04|-1.696334e+02 -1.696336e+02| 0:0:29| spchol  1  1 
47|0.571|0.472|1.0e-12|4.4e-09|4.0e-04|-1.696334e+02 -1.696335e+02| 0:0:29| spchol  1  1 
48|0.573|0.472|8.4e-12|2.4e-09|2.2e-04|-1.696335e+02 -1.696335e+02| 0:0:30| spchol  1  1 
49|0.575|0.471|1.6e-12|1.3e-09|1.2e-04|-1.696335e+02 -1.696335e+02| 0:0:31| spchol  1  1 
50|0.579|0.471|3.8e-11|7.0e-10|6.5e-05|-1.696335e+02 -1.696335e+02| 0:0:31| spchol  1  1 
51|0.583|0.471|3.2e-11|3.8e-10|3.7e-05|-1.696335e+02 -1.696335e+02| 0:0:32| spchol  1  1 
52|0.593|0.471|1.8e-11|2.2e-10|2.2e-05|-1.696335e+02 -1.696335e+02| 0:0:33| spchol  1  1 
53|0.612|0.471|1.4e-11|1.3e-10|1.3e-05|-1.696335e+02 -1.696335e+02| 0:0:33| spchol  1  1 
54|0.634|0.471|2.1e-11|7.7e-11|7.7e-06|-1.696335e+02 -1.696335e+02| 0:0:34| spchol  1  1 
55|0.661|0.471|7.4e-12|4.5e-11|4.5e-06|-1.696335e+02 -1.696335e+02| 0:0:34|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 55
 primal objective value = -1.69633494e+02
 dual   objective value = -1.69633494e+02
 gap := trace(XZ)       = 4.54e-06
 relative gap           = 1.33e-08
 actual relative gap    = 2.33e-09
 rel. primal infeas (scaled problem)   = 7.37e-12
 rel. dual     "        "       "      = 4.52e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.3e+04, 1.2e+07, 1.2e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 34.43  
 CPU time per iteration = 0.63  
 termination code       =  0
 DIMACS: 7.4e-12  0.0e+00  2.5e-10  0.0e+00  2.3e-09  1.3e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +171.553
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.9e+09| 7.448049e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.059|0.239|3.9e+02|9.9e+01|1.2e+09| 1.132699e+06 -6.154510e+04| 0:0:01| spchol  1  1 
 2|0.352|0.495|2.5e+02|5.0e+01|3.1e+08| 2.037422e+06 -1.001201e+05| 0:0:02| spchol  1  1 
 3|0.874|0.825|3.2e+01|8.7e+00|3.6e+07| 2.166749e+06 -1.087225e+05| 0:0:02| spchol  1  1 
 4|0.916|0.906|2.7e+00|8.2e-01|3.2e+06| 5.378778e+05 -9.244117e+04| 0:0:03| spchol  1  1 
 5|0.726|0.656|7.4e-01|2.9e-01|1.0e+06| 1.847941e+05 -5.625428e+04| 0:0:04| spchol  1  1 
 6|0.706|0.398|2.2e-01|1.7e-01|4.2e+05| 7.062508e+04 -3.832439e+04| 0:0:04| spchol  1  1 
 7|0.495|0.326|1.1e-01|1.2e-01|2.5e+05| 4.142745e+04 -2.723789e+04| 0:0:05| spchol  1  1 
 8|0.659|0.454|3.7e-02|6.4e-02|1.2e+05| 1.973260e+04 -1.595468e+04| 0:0:06| spchol  1  1 
 9|0.426|0.386|2.1e-02|4.4e-02|8.0e+04| 1.339135e+04 -1.022963e+04| 0:0:06| spchol  1  1 
10|0.734|0.467|5.7e-03|2.6e-02|3.8e+04| 6.312850e+03 -5.750123e+03| 0:0:07| spchol  1  1 
11|0.803|0.341|1.1e-03|1.8e-02|1.9e+04| 2.822637e+03 -3.898026e+03| 0:0:07| spchol  1  1 
12|0.929|0.349|8.0e-05|1.2e-02|1.0e+04| 1.075470e+03 -2.603993e+03| 0:0:08| spchol  1  1 
13|0.702|0.380|2.4e-05|7.5e-03|6.1e+03| 5.538208e+02 -1.658611e+03| 0:0:09| spchol  1  1 
14|0.381|0.282|1.5e-05|5.4e-03|4.5e+03| 3.856729e+02 -1.216387e+03| 0:0:09| spchol  1  1 
15|0.671|0.191|5.0e-06|5.5e-03|3.4e+03| 1.633220e+02 -1.000353e+03| 0:0:10| spchol  1  1 
16|0.625|0.435|2.0e-06|3.1e-03|2.0e+03| 6.011577e+01 -6.100823e+02| 0:0:10| spchol  1  1 
17|0.565|0.245|9.3e-07|2.4e-03|1.5e+03|-5.755410e+01 -5.140074e+02| 0:0:11| spchol  1  1 
18|0.846|0.310|2.0e-07|1.6e-03|9.3e+02|-1.566059e+02 -4.202244e+02| 0:0:12| spchol  1  1 
19|0.845|0.388|8.2e-08|1.0e-03|5.7e+02|-1.806060e+02 -3.362071e+02| 0:0:12| spchol  1  1 
20|1.000|0.326|6.0e-08|6.7e-04|3.9e+02|-1.893339e+02 -2.919835e+02| 0:0:13| spchol  1  1 
21|1.000|0.357|4.1e-08|4.3e-04|2.5e+02|-1.925503e+02 -2.589903e+02| 0:0:13| spchol  1  1 
22|1.000|0.331|2.8e-08|2.9e-04|1.7e+02|-1.943669e+02 -2.391133e+02| 0:0:14| spchol  1  1 
23|1.000|0.357|1.8e-08|1.9e-04|1.1e+02|-1.956580e+02 -2.246174e+02| 0:0:15| spchol  1  1 
24|1.000|0.357|1.1e-08|1.2e-04|7.2e+01|-1.965085e+02 -2.151968e+02| 0:0:15| spchol  1  1 
25|0.973|0.401|5.6e-09|7.2e-05|4.3e+01|-1.970710e+02 -2.082804e+02| 0:0:16| spchol  1  1 
26|1.000|0.327|3.5e-09|4.8e-05|2.9e+01|-1.973145e+02 -2.048734e+02| 0:0:16| spchol  1  1 
27|1.000|0.377|2.0e-09|3.0e-05|1.8e+01|-1.974685e+02 -2.022018e+02| 0:0:17| spchol  1  1 
28|0.905|0.400|1.1e-09|1.8e-05|1.1e+01|-1.975607e+02 -2.004065e+02| 0:0:18| spchol  1  1 
29|1.000|0.322|6.4e-10|1.2e-05|7.2e+00|-1.976025e+02 -1.995346e+02| 0:0:18| spchol  1  1 
30|1.000|0.347|3.9e-10|8.0e-06|4.7e+00|-1.976271e+02 -1.988938e+02| 0:0:19| spchol  1  1 
31|1.000|0.340|2.7e-10|5.3e-06|3.1e+00|-1.976397e+02 -1.984818e+02| 0:0:19| spchol  1  1 
32|1.000|0.320|1.9e-10|3.6e-06|2.1e+00|-1.976477e+02 -1.982244e+02| 0:0:20| spchol  1  1 
33|1.000|0.334|1.3e-10|2.4e-06|1.4e+00|-1.976532e+02 -1.980401e+02| 0:0:21| spchol  1  1 
34|1.000|0.329|8.7e-11|1.6e-06|9.6e-01|-1.976575e+02 -1.979186e+02| 0:0:21| spchol  1  1 
35|1.000|0.344|5.8e-11|1.1e-06|6.3e-01|-1.976605e+02 -1.978329e+02| 0:0:22| spchol  1  1 
36|1.000|0.352|3.5e-11|3.6e-06|4.1e-01|-1.976627e+02 -1.977748e+02| 0:0:23| spchol  1  1 
37|1.000|0.908|2.2e-11|2.4e-06|5.2e-02|-1.976642e+02 -1.976772e+02| 0:0:23| spchol  1  1 
38|0.568|0.936|1.1e-11|3.0e-07|1.0e-02|-1.976651e+02 -1.976671e+02| 0:0:24| spchol  1  1 
39|0.575|0.472|5.8e-12|5.8e-08|5.3e-03|-1.976656e+02 -1.976667e+02| 0:0:25| spchol  1  1 
40|0.576|0.472|3.8e-12|3.1e-08|2.9e-03|-1.976659e+02 -1.976665e+02| 0:0:25| spchol  1  1 
41|0.578|0.472|2.0e-12|1.7e-08|1.5e-03|-1.976661e+02 -1.976664e+02| 0:0:26| spchol  1  1 
42|0.580|0.472|1.1e-12|8.9e-09|8.3e-04|-1.976661e+02 -1.976663e+02| 0:0:26| spchol  1  1 
43|0.582|0.471|8.2e-12|4.8e-09|4.4e-04|-1.976662e+02 -1.976663e+02| 0:0:27| spchol  1  1 
44|0.584|0.471|8.0e-12|2.6e-09|2.4e-04|-1.976662e+02 -1.976662e+02| 0:0:28| spchol  1  1 
45|0.587|0.471|6.6e-12|1.4e-09|1.3e-04|-1.976662e+02 -1.976662e+02| 0:0:29| spchol  1  1 
46|0.591|0.471|2.4e-11|7.6e-10|7.1e-05|-1.976662e+02 -1.976662e+02| 0:0:29| spchol  1  1 
47|0.597|0.471|1.2e-11|4.2e-10|4.1e-05|-1.976662e+02 -1.976662e+02| 0:0:30| spchol  1  1 
48|0.608|0.471|9.9e-12|2.4e-10|2.4e-05|-1.976662e+02 -1.976662e+02| 0:0:30| spchol  1  1 
49|0.630|0.471|1.6e-11|1.4e-10|1.4e-05|-1.976662e+02 -1.976662e+02| 0:0:31| spchol  2  1 
50|0.656|0.471|2.7e-13|8.3e-11|8.4e-06|-1.976662e+02 -1.976662e+02| 0:0:32| spchol  2  1 
51|0.688|0.471|1.3e-11|4.9e-11|5.0e-06|-1.976662e+02 -1.976662e+02| 0:0:33|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 51
 primal objective value = -1.97666214e+02
 dual   objective value = -1.97666214e+02
 gap := trace(XZ)       = 4.97e-06
 relative gap           = 1.25e-08
 actual relative gap    = 2.18e-09
 rel. primal infeas (scaled problem)   = 1.25e-11
 rel. dual     "        "       "      = 4.89e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 2.7e+04, 1.0e+07, 1.0e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.1e+02
 Total CPU time (secs)  = 32.62  
 CPU time per iteration = 0.64  
 termination code       =  0
 DIMACS: 1.3e-11  0.0e+00  2.4e-10  0.0e+00  2.2e-09  1.3e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +203.335
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.9e+09| 7.454049e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.060|0.243|3.9e+02|9.7e+01|1.2e+09| 1.137648e+06 -6.183265e+04| 0:0:01| spchol  1  1 
 2|0.373|0.502|2.5e+02|4.8e+01|3.0e+08| 2.093065e+06 -1.008595e+05| 0:0:02| spchol  1  1 
 3|0.884|0.831|2.9e+01|8.1e+00|3.3e+07| 2.151439e+06 -1.087855e+05| 0:0:03| spchol  1  1 
 4|0.903|0.904|2.8e+00|7.9e-01|3.3e+06| 5.341997e+05 -9.093908e+04| 0:0:03| spchol  1  1 
 5|0.710|0.657|8.1e-01|2.7e-01|1.1e+06| 1.912843e+05 -5.557101e+04| 0:0:04| spchol  1  1 
 6|0.669|0.373|2.7e-01|1.7e-01|4.7e+05| 7.889528e+04 -3.928950e+04| 0:0:05| spchol  1  1 
 7|0.494|0.321|1.4e-01|1.2e-01|2.8e+05| 4.616634e+04 -2.823719e+04| 0:0:05| spchol  1  1 
 8|0.681|0.420|4.3e-02|6.8e-02|1.3e+05| 2.090317e+04 -1.745628e+04| 0:0:06| spchol  1  1 
 9|0.474|0.456|2.3e-02|4.1e-02|8.0e+04| 1.353822e+04 -1.004586e+04| 0:0:06| spchol  1  1 
10|0.764|0.496|5.4e-03|2.3e-02|3.5e+04| 6.047442e+03 -5.385801e+03| 0:0:07| spchol  1  1 
11|0.800|0.368|1.1e-03|1.6e-02|1.7e+04| 2.634884e+03 -3.510354e+03| 0:0:08| spchol  1  1 
12|0.933|0.321|7.2e-05|1.1e-02|9.4e+03| 9.261649e+02 -2.444141e+03| 0:0:08| spchol  1  1 
13|0.673|0.390|2.4e-05|6.6e-03|5.6e+03| 4.765974e+02 -1.536273e+03| 0:0:09| spchol  1  1 
14|0.378|0.259|1.5e-05|4.9e-03|4.3e+03| 3.273628e+02 -1.163926e+03| 0:0:09| spchol  1  1 
15|0.649|0.206|5.3e-06|3.9e-03|3.2e+03| 1.329307e+02 -9.462169e+02| 0:0:10| spchol  1  1 
16|0.725|0.232|1.6e-06|3.0e-03|2.4e+03|-5.489019e+00 -7.648582e+02| 0:0:11| spchol  1  1 
17|0.825|0.321|4.0e-07|2.0e-03|1.6e+03|-1.315393e+02 -5.935676e+02| 0:0:11| spchol  1  1 
18|0.750|0.428|1.6e-07|1.2e-03|8.9e+02|-1.877076e+02 -4.400327e+02| 0:0:12| spchol  1  1 
19|0.876|0.309|7.6e-08|8.1e-04|6.0e+02|-2.102446e+02 -3.754613e+02| 0:0:12| spchol  1  1 
20|1.000|0.303|6.5e-08|5.6e-04|4.3e+02|-2.166179e+02 -3.309982e+02| 0:0:13| spchol  1  1 
21|1.000|0.371|4.1e-08|3.5e-04|2.7e+02|-2.205794e+02 -2.926930e+02| 0:0:13| spchol  1  1 
22|1.000|0.340|2.8e-08|2.3e-04|1.8e+02|-2.226626e+02 -2.704518e+02| 0:0:14| spchol  1  1 
23|1.000|0.356|1.8e-08|1.5e-04|1.2e+02|-2.240063e+02 -2.548988e+02| 0:0:14| spchol  1  1 
24|1.000|0.372|9.8e-09|9.5e-05|7.4e+01|-2.249068e+02 -2.443266e+02| 0:0:14| spchol  1  1 
25|0.995|0.385|5.2e-09|5.8e-05|4.5e+01|-2.253992e+02 -2.373586e+02| 0:0:15| spchol  1  1 
26|1.000|0.356|3.0e-09|3.7e-05|2.9e+01|-2.256231e+02 -2.333524e+02| 0:0:15| spchol  1  1 
27|0.937|0.402|1.6e-09|2.2e-05|1.7e+01|-2.257705e+02 -2.304023e+02| 0:0:16| spchol  1  1 
28|1.000|0.337|9.1e-10|1.5e-05|1.1e+01|-2.258416e+02 -2.289136e+02| 0:0:16| spchol  1  1 
29|1.000|0.297|7.4e-10|1.0e-05|8.1e+00|-2.258587e+02 -2.280417e+02| 0:0:16| spchol  1  1 
30|1.000|0.312|5.5e-10|7.2e-06|5.6e+00|-2.258780e+02 -2.273938e+02| 0:0:17| spchol  1  1 
31|1.000|0.329|3.9e-10|4.8e-06|3.8e+00|-2.258941e+02 -2.269208e+02| 0:0:17| spchol  1  1 
32|1.000|0.326|2.7e-10|3.3e-06|2.6e+00|-2.259063e+02 -2.266036e+02| 0:0:18| spchol  1  1 
33|1.000|0.336|1.8e-10|2.2e-06|1.7e+00|-2.259149e+02 -2.263819e+02| 0:0:18| spchol  1  1 
34|1.000|0.333|1.2e-10|1.4e-06|1.2e+00|-2.259210e+02 -2.262349e+02| 0:0:18| spchol  1  1 
35|1.000|0.343|8.3e-11|9.5e-07|7.7e-01|-2.259252e+02 -2.261329e+02| 0:0:19| spchol  1  1 
36|1.000|0.344|6.5e-11|6.2e-07|5.0e-01|-2.259281e+02 -2.260652e+02| 0:0:19| spchol  1  1 
37|1.000|0.361|3.6e-11|2.8e-06|3.3e-01|-2.259301e+02 -2.260182e+02| 0:0:19| spchol  1  1 
38|1.000|0.906|1.7e-11|1.9e-06|4.3e-02|-2.259314e+02 -2.259420e+02| 0:0:20| spchol  1  1 
39|0.569|0.935|9.3e-12|2.4e-07|8.4e-03|-2.259322e+02 -2.259338e+02| 0:0:20| spchol  1  1 
40|0.574|0.472|4.8e-12|4.8e-08|4.4e-03|-2.259326e+02 -2.259335e+02| 0:0:21| spchol  1  1 
41|0.575|0.471|3.1e-12|2.5e-08|2.4e-03|-2.259328e+02 -2.259333e+02| 0:0:21| spchol  1  1 
42|0.577|0.471|2.0e-12|1.4e-08|1.3e-03|-2.259330e+02 -2.259332e+02| 0:0:21| spchol  1  1 
43|0.579|0.471|3.8e-11|7.3e-09|6.9e-04|-2.259330e+02 -2.259332e+02| 0:0:21| spchol  1  1 
44|0.582|0.471|2.1e-11|3.9e-09|3.7e-04|-2.259331e+02 -2.259331e+02| 0:0:22| spchol  1  1 
45|0.584|0.471|8.2e-11|2.1e-09|2.0e-04|-2.259331e+02 -2.259331e+02| 0:0:22| spchol  1  1 
46|0.588|0.471|3.4e-11|1.2e-09|1.1e-04|-2.259331e+02 -2.259331e+02| 0:0:23| spchol  1  1 
47|0.595|0.471|8.8e-11|6.4e-10|6.6e-05|-2.259331e+02 -2.259331e+02| 0:0:23| spchol  1  1 
48|0.614|0.471|4.3e-11|3.8e-10|3.9e-05|-2.259331e+02 -2.259331e+02| 0:0:23| spchol  1  1 
49|0.636|0.471|1.0e-11|2.2e-10|2.3e-05|-2.259331e+02 -2.259331e+02| 0:0:23| spchol  1  1 
50|0.663|0.471|1.5e-11|1.3e-10|1.4e-05|-2.259331e+02 -2.259331e+02| 0:0:24| spchol  1  1 
51|0.697|0.471|2.8e-11|7.8e-11|8.0e-06|-2.259331e+02 -2.259331e+02| 0:0:24| spchol  2  1 
52|0.739|0.471|3.8e-11|4.6e-11|4.8e-06|-2.259331e+02 -2.259331e+02| 0:0:25|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 52
 primal objective value = -2.25933102e+02
 dual   objective value = -2.25933103e+02
 gap := trace(XZ)       = 4.76e-06
 relative gap           = 1.05e-08
 actual relative gap    = 1.63e-09
 rel. primal infeas (scaled problem)   = 3.77e-11
 rel. dual     "        "       "      = 4.63e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 2.7e+04, 1.0e+07, 1.0e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.1e+02
 Total CPU time (secs)  = 24.56  
 CPU time per iteration = 0.47  
 termination code       =  0
 DIMACS: 3.8e-11  0.0e+00  2.1e-10  0.0e+00  1.6e-09  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +235.852
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.4e+02|6.8e+09| 7.417588e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.053|0.224|4.0e+02|1.1e+02|1.3e+09| 1.116607e+06 -6.094135e+04| 0:0:01| spchol  1  1 
 2|0.295|0.468|2.8e+02|5.6e+01|3.3e+08| 1.880174e+06 -9.774490e+04| 0:0:01| spchol  1  1 
 3|0.850|0.820|4.2e+01|1.0e+01|4.3e+07| 2.159210e+06 -1.074210e+05| 0:0:02| spchol  1  1 
 4|0.900|0.908|4.2e+00|9.4e-01|4.3e+06| 6.079371e+05 -9.456179e+04| 0:0:02| spchol  1  1 
 5|0.690|0.593|1.3e+00|3.8e-01|1.6e+06| 2.366991e+05 -6.798803e+04| 0:0:03| spchol  1  1 
 6|0.788|0.484|2.7e-01|2.0e-01|4.9e+05| 7.617864e+04 -4.375289e+04| 0:0:03| spchol  1  1 
 7|0.451|0.323|1.5e-01|1.4e-01|3.1e+05| 4.708556e+04 -3.124082e+04| 0:0:04| spchol  1  1 
 8|0.570|0.345|6.5e-02|8.9e-02|1.7e+05| 2.521897e+04 -2.156791e+04| 0:0:04| spchol  1  1 
 9|0.667|0.359|2.2e-02|6.2e-02|9.5e+04| 1.245059e+04 -1.444224e+04| 0:0:04| spchol  1  1 
10|0.647|0.519|7.6e-03|3.3e-02|4.9e+04| 7.259860e+03 -7.395690e+03| 0:0:05| spchol  1  1 
11|0.835|0.424|1.3e-03|2.0e-02|2.3e+04| 3.332516e+03 -4.421922e+03| 0:0:05| spchol  1  1 
12|0.713|0.298|3.6e-04|1.4e-02|1.4e+04| 1.907619e+03 -3.181030e+03| 0:0:06| spchol  1  1 
13|0.498|0.304|1.8e-04|1.0e-02|9.9e+03| 1.296868e+03 -2.265857e+03| 0:0:06| spchol  1  1 
14|0.372|0.240|1.1e-04|7.6e-03|7.5e+03| 9.623812e+02 -1.752572e+03| 0:0:07| spchol  1  1 
15|0.589|0.176|4.7e-05|8.0e-03|5.7e+03| 5.476445e+02 -1.462040e+03| 0:0:07| spchol  1  1 
16|0.948|0.465|2.4e-06|4.3e-03|2.7e+03| 1.682652e+02 -8.131722e+02| 0:0:08| spchol  1  1 
17|0.626|0.305|1.0e-06|3.0e-03|2.0e+03| 8.311367e+01 -5.788677e+02| 0:0:08| spchol  1  1 
18|0.540|0.267|5.3e-07|2.2e-03|1.5e+03| 5.257680e+01 -4.341563e+02| 0:0:08| spchol  1  1 
19|0.870|0.299|1.2e-07|1.5e-03|9.8e+02| 1.477424e+01 -3.120167e+02| 0:0:09| spchol  1  1 
20|1.000|0.298|1.2e-07|1.1e-03|7.2e+02|-1.726164e+00 -2.273671e+02| 0:0:09| spchol  1  1 
21|1.000|0.318|8.5e-08|7.4e-04|4.9e+02|-3.273672e+01 -1.718451e+02| 0:0:10| spchol  1  1 
22|1.000|0.418|4.4e-08|4.3e-04|2.8e+02|-5.290350e+01 -1.260476e+02| 0:0:10| spchol  1  1 
23|1.000|0.401|2.2e-08|2.6e-04|1.6e+02|-5.687757e+01 -1.000673e+02| 0:0:11| spchol  1  1 
24|1.000|0.386|1.2e-08|1.6e-04|1.0e+02|-5.839267e+01 -8.489938e+01| 0:0:11| spchol  1  1 
25|1.000|0.329|8.0e-09|1.1e-04|6.7e+01|-5.897711e+01 -7.686347e+01| 0:0:12| spchol  1  1 
26|1.000|0.319|5.8e-09|7.2e-05|4.6e+01|-5.924350e+01 -7.158504e+01| 0:0:12| spchol  1  1 
27|1.000|0.309|4.3e-09|5.0e-05|3.2e+01|-5.942897e+01 -6.807932e+01| 0:0:13| spchol  1  1 
28|1.000|0.325|3.1e-09|3.4e-05|2.2e+01|-5.958582e+01 -6.551171e+01| 0:0:13| spchol  1  1 
29|1.000|0.336|2.0e-09|2.2e-05|1.5e+01|-5.973013e+01 -6.369995e+01| 0:0:13| spchol  1  1 
30|1.000|0.362|1.3e-09|1.4e-05|9.5e+00|-5.983350e+01 -6.238885e+01| 0:0:14| spchol  1  1 
31|1.000|0.326|8.5e-10|9.6e-06|6.5e+00|-5.989159e+01 -6.162720e+01| 0:0:14| spchol  1  1 
32|1.000|0.382|4.9e-10|5.9e-06|4.0e+00|-5.993823e+01 -6.101799e+01| 0:0:15| spchol  1  1 
33|0.912|0.395|2.6e-10|3.6e-06|2.4e+00|-5.996671e+01 -6.062154e+01| 0:0:15| spchol  1  1 
34|1.000|0.358|1.4e-10|2.3e-06|1.5e+00|-5.998138e+01 -6.040177e+01| 0:0:16| spchol  1  1 
35|1.000|0.341|8.8e-11|1.5e-06|1.0e+00|-5.998835e+01 -6.026649e+01| 0:0:16| spchol  1  1 
36|1.000|0.403|4.9e-11|9.1e-07|6.0e-01|-5.999325e+01 -6.015990e+01| 0:0:16| spchol  1  1 
37|1.000|0.317|3.3e-11|3.7e-06|4.1e-01|-5.999520e+01 -6.010953e+01| 0:0:17| spchol  1  1 
38|1.000|0.922|2.8e-11|2.5e-06|5.7e-02|-5.999577e+01 -6.000949e+01| 0:0:17| spchol  1  1 
39|0.613|0.942|1.5e-11|3.5e-07|1.5e-02|-5.999738e+01 -6.000017e+01| 0:0:18| spchol  1  1 
40|0.560|0.472|8.0e-12|8.9e-08|7.8e-03|-5.999823e+01 -5.999977e+01| 0:0:18| spchol  1  1 
41|0.561|0.472|4.5e-12|4.8e-08|4.2e-03|-5.999867e+01 -5.999953e+01| 0:0:19| spchol  1  1 
42|0.563|0.472|2.6e-12|2.6e-08|2.2e-03|-5.999891e+01 -5.999938e+01| 0:0:19| spchol  1  1 
43|0.565|0.472|5.4e-12|1.4e-08|1.2e-03|-5.999904e+01 -5.999930e+01| 0:0:19| spchol  1  1 
44|0.566|0.472|9.1e-12|7.4e-09|6.5e-04|-5.999910e+01 -5.999925e+01| 0:0:20| spchol  1  1 
45|0.568|0.472|1.0e-11|4.0e-09|3.5e-04|-5.999914e+01 -5.999922e+01| 0:0:20| spchol  1  1 
46|0.571|0.471|1.2e-11|2.1e-09|1.9e-04|-5.999916e+01 -5.999920e+01| 0:0:21| spchol  1  1 
47|0.574|0.471|2.2e-11|1.2e-09|1.1e-04|-5.999917e+01 -5.999919e+01| 0:0:21| spchol  1  1 
48|0.580|0.471|8.6e-13|6.5e-10|6.2e-05|-5.999917e+01 -5.999918e+01| 0:0:22| spchol  1  1 
49|0.595|0.471|2.1e-12|3.8e-10|3.5e-05|-5.999917e+01 -5.999918e+01| 0:0:22| spchol  1  1 
50|0.605|0.471|4.3e-13|2.1e-10|2.0e-05|-5.999918e+01 -5.999918e+01| 0:0:23| spchol  1  1 
51|0.618|0.471|4.1e-12|1.2e-10|1.2e-05|-5.999918e+01 -5.999918e+01| 0:0:23| spchol  1  1 
52|0.642|0.471|3.6e-12|7.4e-11|7.2e-06|-5.999918e+01 -5.999918e+01| 0:0:23| spchol  1  1 
53|0.672|0.471|6.5e-12|4.4e-11|4.2e-06|-5.999918e+01 -5.999918e+01| 0:0:24| spchol  1  1 
54|0.708|0.471|1.5e-12|2.6e-11|2.5e-06|-5.999918e+01 -5.999918e+01| 0:0:24| spchol  1  1 
55|0.754|0.471|5.3e-12|1.5e-11|1.5e-06|-5.999918e+01 -5.999918e+01| 0:0:25|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 55
 primal objective value = -5.99991768e+01
 dual   objective value = -5.99991770e+01
 gap := trace(XZ)       = 1.49e-06
 relative gap           = 1.23e-08
 actual relative gap    = 1.80e-09
 rel. primal infeas (scaled problem)   = 5.28e-12
 rel. dual     "        "       "      = 1.54e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 4.0e+04, 1.2e+07, 1.2e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 24.81  
 CPU time per iteration = 0.45  
 termination code       =  0
 DIMACS: 5.3e-12  0.0e+00  1.6e-10  0.0e+00  1.8e-09  1.2e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +46.8778
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.423588e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.053|0.226|4.0e+02|1.0e+02|1.3e+09| 1.118922e+06 -6.094689e+04| 0:0:01| spchol  1  1 
 2|0.301|0.471|2.8e+02|5.5e+01|3.2e+08| 1.896970e+06 -9.796253e+04| 0:0:01| spchol  1  1 
 3|0.852|0.819|4.1e+01|1.0e+01|4.3e+07| 2.168197e+06 -1.076763e+05| 0:0:02| spchol  1  1 
 4|0.908|0.908|3.8e+00|9.2e-01|4.0e+06| 5.956624e+05 -9.451305e+04| 0:0:02| spchol  1  1 
 5|0.692|0.596|1.2e+00|3.8e-01|1.5e+06| 2.286215e+05 -6.610746e+04| 0:0:02| spchol  1  1 
 6|0.784|0.480|2.5e-01|2.0e-01|4.6e+05| 7.402213e+04 -4.222887e+04| 0:0:03| spchol  1  1 
 7|0.444|0.312|1.4e-01|1.4e-01|2.9e+05| 4.623234e+04 -3.050033e+04| 0:0:03| spchol  1  1 
 8|0.569|0.348|6.0e-02|8.8e-02|1.6e+05| 2.495269e+04 -2.093663e+04| 0:0:03| spchol  1  1 
 9|0.647|0.357|2.1e-02|6.2e-02|9.3e+04| 1.275889e+04 -1.407000e+04| 0:0:04| spchol  1  1 
10|0.627|0.515|7.9e-03|3.3e-02|4.9e+04| 7.558478e+03 -7.263835e+03| 0:0:04| spchol  1  1 
11|0.781|0.416|1.7e-03|2.0e-02|2.4e+04| 3.671201e+03 -4.403211e+03| 0:0:04| spchol  1  1 
12|0.756|0.282|4.2e-04|1.5e-02|1.5e+04| 1.918647e+03 -3.233700e+03| 0:0:05| spchol  1  1 
13|0.529|0.338|2.0e-04|1.0e-02|9.6e+03| 1.251958e+03 -2.197597e+03| 0:0:05| spchol  1  1 
14|0.378|0.250|1.2e-04|7.5e-03|7.3e+03| 9.127681e+02 -1.681330e+03| 0:0:06| spchol  1  1 
15|0.618|0.180|4.7e-05|7.9e-03|5.4e+03| 4.889577e+02 -1.397273e+03| 0:0:06| spchol  1  1 
16|0.938|0.482|2.9e-06|4.1e-03|2.5e+03| 1.467186e+02 -7.560717e+02| 0:0:06| spchol  1  1 
17|0.541|0.303|1.4e-06|2.9e-03|1.8e+03| 7.858578e+01 -5.408436e+02| 0:0:07| spchol  1  1 
18|0.634|0.240|5.7e-07|2.2e-03|1.4e+03| 4.098990e+01 -4.212376e+02| 0:0:07| spchol  1  1 
19|1.000|0.305|8.0e-08|1.5e-03|9.2e+02|-8.778529e+00 -3.070468e+02| 0:0:07| spchol  1  1 
20|1.000|0.337|1.3e-07|1.0e-03|6.5e+02|-5.886272e+01 -2.322897e+02| 0:0:08| spchol  1  1 
21|1.000|0.424|4.9e-08|5.8e-04|3.5e+02|-7.889853e+01 -1.723042e+02| 0:0:08| spchol  1  1 
22|1.000|0.376|3.3e-08|3.6e-04|2.2e+02|-8.305405e+01 -1.411203e+02| 0:0:09| spchol  1  1 
23|1.000|0.409|1.6e-08|2.1e-04|1.3e+02|-8.545000e+01 -1.195706e+02| 0:0:09| spchol  1  1 
24|1.000|0.336|1.1e-08|1.4e-04|8.7e+01|-8.624966e+01 -1.090385e+02| 0:0:09| spchol  1  1 
25|1.000|0.320|7.4e-09|9.6e-05|6.0e+01|-8.664002e+01 -1.022991e+02| 0:0:10| spchol  1  1 
26|1.000|0.312|5.6e-09|6.6e-05|4.2e+01|-8.686180e+01 -9.779906e+01| 0:0:10| spchol  1  1 
27|1.000|0.311|4.1e-09|4.6e-05|2.9e+01|-8.704157e+01 -9.468999e+01| 0:0:10| spchol  1  1 
28|1.000|0.334|2.9e-09|3.0e-05|2.0e+01|-8.720194e+01 -9.236603e+01| 0:0:11| spchol  1  1 
29|1.000|0.350|1.8e-09|2.0e-05|1.3e+01|-8.734463e+01 -9.072449e+01| 0:0:11| spchol  1  1 
30|1.000|0.349|1.2e-09|1.3e-05|8.4e+00|-8.742419e+01 -8.964615e+01| 0:0:12| spchol  1  1 
31|1.000|0.327|7.7e-10|8.7e-06|5.7e+00|-8.747462e+01 -8.898266e+01| 0:0:12| spchol  1  1 
32|1.000|0.399|4.1e-10|5.2e-06|3.4e+00|-8.751887e+01 -8.842950e+01| 0:0:12| spchol  1  1 
33|0.886|0.401|2.2e-10|3.1e-06|2.0e+00|-8.754183e+01 -8.808863e+01| 0:0:13| spchol  1  1 
34|1.000|0.337|1.2e-10|2.1e-06|1.3e+00|-8.755360e+01 -8.791613e+01| 0:0:13| spchol  1  1 
35|1.000|0.337|7.9e-11|1.4e-06|8.9e-01|-8.755908e+01 -8.780068e+01| 0:0:13| spchol  1  1 
36|1.000|0.393|4.4e-11|8.3e-07|5.4e-01|-8.756323e+01 -8.771048e+01| 0:0:14| spchol  1  1 
37|1.000|0.285|3.7e-11|3.3e-06|3.9e-01|-8.756431e+01 -8.767064e+01| 0:0:14| spchol  1  1 
38|1.000|0.915|2.8e-11|2.4e-06|5.7e-02|-8.756511e+01 -8.757873e+01| 0:0:14| spchol  1  1 
39|0.607|0.942|1.5e-11|3.5e-07|1.4e-02|-8.756669e+01 -8.756942e+01| 0:0:15| spchol  1  1 
40|0.560|0.472|7.9e-12|8.7e-08|7.7e-03|-8.756752e+01 -8.756903e+01| 0:0:15| spchol  1  1 
41|0.562|0.472|6.4e-12|4.7e-08|4.1e-03|-8.756796e+01 -8.756880e+01| 0:0:15| spchol  1  1 
42|0.563|0.472|7.5e-12|2.5e-08|2.2e-03|-8.756819e+01 -8.756865e+01| 0:0:16| spchol  1  1 
43|0.565|0.472|8.2e-12|1.3e-08|1.2e-03|-8.756831e+01 -8.756857e+01| 0:0:16| spchol  1  1 
44|0.567|0.472|9.4e-12|7.2e-09|6.4e-04|-8.756838e+01 -8.756852e+01| 0:0:17| spchol  1  1 
45|0.569|0.472|1.1e-11|3.9e-09|3.4e-04|-8.756841e+01 -8.756849e+01| 0:0:17| spchol  1  1 
46|0.571|0.471|2.7e-12|2.1e-09|1.9e-04|-8.756843e+01 -8.756847e+01| 0:0:17| spchol  1  1 
47|0.575|0.471|7.5e-12|1.1e-09|1.0e-04|-8.756844e+01 -8.756847e+01| 0:0:18| spchol  1  1 
48|0.578|0.471|4.2e-12|6.2e-10|5.7e-05|-8.756845e+01 -8.756846e+01| 0:0:18| spchol  1  1 
49|0.585|0.471|1.4e-11|3.5e-10|3.2e-05|-8.756845e+01 -8.756846e+01| 0:0:18| spchol  1  1 
50|0.595|0.471|1.4e-11|2.0e-10|1.9e-05|-8.756845e+01 -8.756845e+01| 0:0:19| spchol  1  1 
51|0.609|0.471|2.9e-11|1.2e-10|1.1e-05|-8.756845e+01 -8.756845e+01| 0:0:19| spchol  1  1 
52|0.631|0.471|1.8e-11|6.9e-11|6.7e-06|-8.756845e+01 -8.756845e+01| 0:0:19| spchol  1  1 
53|0.658|0.471|8.4e-12|4.1e-11|4.0e-06|-8.756845e+01 -8.756845e+01| 0:0:20| spchol  1  1 
54|0.691|0.471|1.0e-11|2.4e-11|2.3e-06|-8.756845e+01 -8.756845e+01| 0:0:20|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 54
 primal objective value = -8.75684523e+01
 dual   objective value = -8.75684527e+01
 gap := trace(XZ)       = 2.34e-06
 relative gap           = 1.33e-08
 actual relative gap    = 2.13e-09
 rel. primal infeas (scaled problem)   = 1.04e-11
 rel. dual     "        "       "      = 2.41e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.8e+04, 1.2e+07, 1.2e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 20.14  
 CPU time per iteration = 0.37  
 termination code       =  0
 DIMACS: 1.0e-11  0.0e+00  2.3e-10  0.0e+00  2.1e-09  1.3e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +76.1971
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.429588e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.054|0.229|3.9e+02|1.0e+02|1.3e+09| 1.121871e+06 -6.101291e+04| 0:0:01| spchol  1  1 
 2|0.309|0.476|2.7e+02|5.4e+01|3.2e+08| 1.920244e+06 -9.832141e+04| 0:0:01| spchol  1  1 
 3|0.855|0.818|4.0e+01|9.9e+00|4.2e+07| 2.180008e+06 -1.080818e+05| 0:0:01| spchol  1  1 
 4|0.916|0.909|3.3e+00|9.1e-01|3.7e+06| 5.821009e+05 -9.448914e+04| 0:0:02| spchol  1  1 
 5|0.697|0.604|1.0e+00|3.6e-01|1.3e+06| 2.185976e+05 -6.381690e+04| 0:0:02| spchol  1  1 
 6|0.779|0.474|2.2e-01|1.9e-01|4.3e+05| 7.120355e+04 -4.044693e+04| 0:0:02| spchol  1  1 
 7|0.433|0.299|1.3e-01|1.3e-01|2.8e+05| 4.521081e+04 -2.968022e+04| 0:0:03| spchol  1  1 
 8|0.571|0.347|5.4e-02|8.8e-02|1.6e+05| 2.448329e+04 -2.038003e+04| 0:0:03| spchol  1  1 
 9|0.626|0.374|2.0e-02|6.0e-02|9.1e+04| 1.298100e+04 -1.335933e+04| 0:0:04| spchol  1  1 
10|0.607|0.493|8.0e-03|3.3e-02|4.9e+04| 7.787674e+03 -7.175663e+03| 0:0:04| spchol  1  1 
11|0.749|0.413|2.0e-03|2.1e-02|2.5e+04| 3.891145e+03 -4.371424e+03| 0:0:04| spchol  1  1 
12|0.796|0.294|4.1e-04|1.5e-02|1.4e+04| 1.868143e+03 -3.159299e+03| 0:0:05| spchol  1  1 
13|0.508|0.355|2.0e-04|9.7e-03|9.2e+03| 1.229388e+03 -2.093745e+03| 0:0:05| spchol  1  1 
14|0.413|0.250|1.2e-04|7.3e-03|6.8e+03| 8.470940e+02 -1.600341e+03| 0:0:05| spchol  1  1 
15|0.609|0.182|4.6e-05|7.7e-03|5.1e+03| 4.491709e+02 -1.325865e+03| 0:0:06| spchol  1  1 
16|0.923|0.469|3.6e-06|4.1e-03|2.5e+03| 1.354297e+02 -7.360660e+02| 0:0:06| spchol  1  1 
17|0.571|0.309|1.6e-06|2.8e-03|1.8e+03| 6.644638e+01 -5.250620e+02| 0:0:06| spchol  1  1 
18|0.660|0.247|5.9e-07|2.1e-03|1.3e+03| 1.958906e+01 -4.121825e+02| 0:0:07| spchol  1  1 
19|1.000|0.298|8.6e-08|1.5e-03|8.6e+02|-6.969484e+01 -3.217036e+02| 0:0:07| spchol  1  1 
20|1.000|0.447|8.4e-08|8.3e-04|4.9e+02|-1.025302e+02 -2.311900e+02| 0:0:08| spchol  1  1 
21|1.000|0.373|4.5e-08|5.2e-04|3.1e+02|-1.086957e+02 -1.888493e+02| 0:0:08| spchol  1  1 
22|1.000|0.378|2.8e-08|3.2e-04|1.9e+02|-1.116630e+02 -1.615341e+02| 0:0:08| spchol  1  1 
23|1.000|0.366|1.6e-08|2.1e-04|1.2e+02|-1.132200e+02 -1.448575e+02| 0:0:09| spchol  1  1 
24|1.000|0.321|1.1e-08|1.4e-04|8.3e+01|-1.138508e+02 -1.355170e+02| 0:0:09| spchol  1  1 
25|1.000|0.323|8.0e-09|9.4e-05|5.7e+01|-1.142297e+02 -1.290802e+02| 0:0:10| spchol  1  1 
26|1.000|0.312|5.9e-09|6.5e-05|4.0e+01|-1.144638e+02 -1.248382e+02| 0:0:10| spchol  1  1 
27|1.000|0.317|4.3e-09|4.4e-05|2.8e+01|-1.146500e+02 -1.218379e+02| 0:0:11| spchol  1  1 
28|1.000|0.339|2.9e-09|2.9e-05|1.8e+01|-1.148145e+02 -1.196235e+02| 0:0:11| spchol  1  1 
29|1.000|0.359|1.7e-09|1.9e-05|1.2e+01|-1.149547e+02 -1.180488e+02| 0:0:11| spchol  1  1 
30|1.000|0.329|1.2e-09|1.3e-05|8.0e+00|-1.150149e+02 -1.171179e+02| 0:0:12| spchol  1  1 
31|1.000|0.325|8.2e-10|8.5e-06|5.5e+00|-1.150604e+02 -1.164944e+02| 0:0:12| spchol  1  1 
32|1.000|0.389|4.5e-10|5.2e-06|3.3e+00|-1.151020e+02 -1.159820e+02| 0:0:12| spchol  1  1 
33|0.892|0.401|2.4e-10|3.1e-06|2.0e+00|-1.151251e+02 -1.156536e+02| 0:0:13| spchol  1  1 
34|0.853|0.389|1.3e-10|1.9e-06|1.2e+00|-1.151376e+02 -1.154605e+02| 0:0:13| spchol  1  1 
35|1.000|0.280|7.9e-11|1.4e-06|8.6e-01|-1.151431e+02 -1.153754e+02| 0:0:14| spchol  1  1 
36|1.000|0.323|6.2e-11|9.3e-07|5.9e-01|-1.151451e+02 -1.153043e+02| 0:0:14| spchol  1  1 
37|1.000|0.317|4.6e-11|3.5e-06|4.1e-01|-1.151471e+02 -1.152568e+02| 0:0:14| spchol  1  1 
38|1.000|0.916|3.1e-11|2.5e-06|5.8e-02|-1.151484e+02 -1.151623e+02| 0:0:15| spchol  1  1 
39|0.614|0.939|1.7e-11|3.5e-07|1.5e-02|-1.151500e+02 -1.151528e+02| 0:0:15| spchol  1  1 
40|0.561|0.472|9.3e-12|8.9e-08|7.9e-03|-1.151509e+02 -1.151524e+02| 0:0:16| spchol  1  1 
41|0.563|0.472|7.7e-12|4.7e-08|4.2e-03|-1.151513e+02 -1.151522e+02| 0:0:16| spchol  1  1 
42|0.564|0.472|5.9e-12|2.5e-08|2.3e-03|-1.151515e+02 -1.151520e+02| 0:0:16| spchol  1  1 
43|0.566|0.472|7.3e-12|1.4e-08|1.2e-03|-1.151517e+02 -1.151519e+02| 0:0:17| spchol  1  1 
44|0.568|0.472|4.2e-11|7.3e-09|6.5e-04|-1.151517e+02 -1.151519e+02| 0:0:17| spchol  1  1 
45|0.570|0.472|4.5e-11|3.9e-09|3.5e-04|-1.151518e+02 -1.151518e+02| 0:0:17| spchol  1  1 
46|0.572|0.472|8.8e-12|2.1e-09|1.9e-04|-1.151518e+02 -1.151518e+02| 0:0:18| spchol  1  1 
47|0.577|0.471|2.2e-11|1.2e-09|1.1e-04|-1.151518e+02 -1.151518e+02| 0:0:18| spchol  1  1 
48|0.582|0.471|8.0e-11|6.4e-10|6.1e-05|-1.151518e+02 -1.151518e+02| 0:0:19| spchol  1  1 
49|0.593|0.471|4.5e-11|3.7e-10|3.6e-05|-1.151518e+02 -1.151518e+02| 0:0:19| spchol  1  1 
50|0.611|0.471|2.8e-11|2.2e-10|2.1e-05|-1.151518e+02 -1.151518e+02| 0:0:19| spchol  1  1 
51|0.628|0.471|1.3e-11|1.3e-10|1.3e-05|-1.151518e+02 -1.151518e+02| 0:0:20| spchol  1  1 
52|0.654|0.471|2.7e-13|7.6e-11|7.5e-06|-1.151518e+02 -1.151518e+02| 0:0:20| spchol  1  1 
53|0.687|0.471|7.8e-12|4.5e-11|4.4e-06|-1.151518e+02 -1.151518e+02| 0:0:20| spchol  1  1 
54|0.726|0.471|3.2e-12|2.7e-11|2.6e-06|-1.151518e+02 -1.151518e+02| 0:0:21|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 54
 primal objective value = -1.15151800e+02
 dual   objective value = -1.15151800e+02
 gap := trace(XZ)       = 2.63e-06
 relative gap           = 1.14e-08
 actual relative gap    = 1.71e-09
 rel. primal infeas (scaled problem)   = 3.21e-12
 rel. dual     "        "       "      = 2.68e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.6e+04, 1.1e+07, 1.1e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 20.54  
 CPU time per iteration = 0.38  
 termination code       =  0
 DIMACS: 3.2e-12  0.0e+00  2.0e-10  0.0e+00  1.7e-09  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +106.03
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.435588e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.056|0.232|3.9e+02|1.0e+02|1.3e+09| 1.125410e+06 -6.114204e+04| 0:0:01| spchol  1  1 
 2|0.320|0.481|2.7e+02|5.3e+01|3.2e+08| 1.950378e+06 -9.880784e+04| 0:0:01| spchol  1  1 
 3|0.859|0.819|3.8e+01|9.6e+00|4.1e+07| 2.181742e+06 -1.083550e+05| 0:0:02| spchol  1  1 
 4|0.922|0.909|2.9e+00|8.8e-01|3.4e+06| 5.634144e+05 -9.415586e+04| 0:0:02| spchol  1  1 
 5|0.709|0.619|8.5e-01|3.4e-01|1.2e+06| 2.035359e+05 -6.078899e+04| 0:0:03| spchol  1  1 
 6|0.774|0.470|1.9e-01|1.8e-01|3.9e+05| 6.662415e+04 -3.813290e+04| 0:0:03| spchol  1  1 
 7|0.421|0.286|1.1e-01|1.3e-01|2.6e+05| 4.304473e+04 -2.836413e+04| 0:0:03| spchol  1  1 
 8|0.610|0.354|4.4e-02|8.4e-02|1.4e+05| 2.209314e+04 -1.924984e+04| 0:0:04| spchol  1  1 
 9|0.576|0.468|1.8e-02|4.9e-02|7.9e+04| 1.270382e+04 -1.089543e+04| 0:0:04| spchol  1  1 
10|0.600|0.390|7.4e-03|3.3e-02|4.7e+04| 7.489036e+03 -6.936297e+03| 0:0:05| spchol  1  1 
11|0.801|0.414|1.5e-03|2.0e-02|2.2e+04| 3.452962e+03 -4.223194e+03| 0:0:05| spchol  1  1 
12|0.879|0.316|1.8e-04|1.4e-02|1.2e+04| 1.469704e+03 -2.962542e+03| 0:0:05| spchol  1  1 
13|0.470|0.380|9.5e-05|8.8e-03|7.8e+03| 1.000713e+03 -1.890660e+03| 0:0:06| spchol  1  1 
14|0.443|0.249|5.3e-05|6.6e-03|5.8e+03| 6.572485e+02 -1.446783e+03| 0:0:06| spchol  1  1 
15|0.675|0.197|1.7e-05|6.9e-03|4.2e+03| 3.019440e+02 -1.178426e+03| 0:0:07| spchol  1  1 
16|0.860|0.464|2.4e-06|3.7e-03|2.2e+03| 9.638746e+01 -6.616089e+02| 0:0:07| spchol  1  1 
17|0.593|0.284|1.1e-06|2.6e-03|1.6e+03| 3.293273e+01 -4.959240e+02| 0:0:08| spchol  1  1 
18|0.642|0.272|4.3e-07|1.9e-03|1.1e+03|-4.318935e+01 -3.985338e+02| 0:0:08| spchol  1  1 
19|0.762|0.333|1.4e-07|1.3e-03|7.2e+02|-1.063001e+02 -3.164180e+02| 0:0:08| spchol  1  1 
20|1.000|0.320|7.4e-08|8.7e-04|4.9e+02|-1.315784e+02 -2.622530e+02| 0:0:09| spchol  1  1 
21|1.000|0.358|5.1e-08|5.6e-04|3.2e+02|-1.360974e+02 -2.204228e+02| 0:0:09| spchol  1  1 
22|1.000|0.379|3.1e-08|3.5e-04|2.0e+02|-1.390940e+02 -1.915398e+02| 0:0:10| spchol  1  1 
23|1.000|0.371|1.8e-08|2.2e-04|1.2e+02|-1.407598e+02 -1.737569e+02| 0:0:10| spchol  1  1 
24|1.000|0.317|1.3e-08|1.5e-04|8.6e+01|-1.413364e+02 -1.641503e+02| 0:0:10| spchol  1  1 
25|1.000|0.312|9.7e-09|1.0e-04|6.0e+01|-1.417296e+02 -1.576215e+02| 0:0:11| spchol  1  1 
26|1.000|0.321|7.1e-09|7.0e-05|4.2e+01|-1.420057e+02 -1.529617e+02| 0:0:11| spchol  1  1 
27|1.000|0.322|5.0e-09|4.7e-05|2.9e+01|-1.422232e+02 -1.497525e+02| 0:0:12| spchol  1  1 
28|1.000|0.339|3.3e-09|3.1e-05|1.9e+01|-1.424007e+02 -1.474385e+02| 0:0:12| spchol  1  1 
29|1.000|0.354|2.0e-09|2.0e-05|1.2e+01|-1.425452e+02 -1.458174e+02| 0:0:13| spchol  1  1 
30|1.000|0.340|1.3e-09|1.3e-05|8.2e+00|-1.426185e+02 -1.448024e+02| 0:0:13| spchol  1  1 
31|0.963|0.388|7.1e-10|8.2e-06|5.0e+00|-1.426832e+02 -1.440237e+02| 0:0:13| spchol  1  1 
32|1.000|0.355|4.1e-10|5.3e-06|3.2e+00|-1.427140e+02 -1.435819e+02| 0:0:14| spchol  1  1 
33|1.000|0.301|3.1e-10|3.7e-06|2.3e+00|-1.427247e+02 -1.433385e+02| 0:0:14| spchol  1  1 
34|1.000|0.337|2.2e-10|2.4e-06|1.5e+00|-1.427349e+02 -1.431463e+02| 0:0:15| spchol  1  1 
35|1.000|0.342|1.4e-10|1.6e-06|1.0e+00|-1.427432e+02 -1.430158e+02| 0:0:15| spchol  1  1 
36|0.981|0.390|7.5e-11|9.8e-07|6.1e-01|-1.427496e+02 -1.429165e+02| 0:0:16| spchol  1  1 
37|1.000|0.337|6.2e-11|3.6e-06|4.1e-01|-1.427525e+02 -1.428636e+02| 0:0:16| spchol  1  1 
38|1.000|0.908|3.5e-11|2.4e-06|6.2e-02|-1.427536e+02 -1.427686e+02| 0:0:16| spchol  1  1 
39|0.636|0.938|1.9e-11|3.7e-07|1.6e-02|-1.427553e+02 -1.427583e+02| 0:0:17| spchol  1  1 
40|0.562|0.472|1.6e-11|9.3e-08|8.3e-03|-1.427562e+02 -1.427579e+02| 0:0:17| spchol  1  1 
41|0.564|0.472|7.8e-12|4.9e-08|4.4e-03|-1.427566e+02 -1.427576e+02| 0:0:18| spchol  1  1 
42|0.566|0.472|6.3e-12|2.6e-08|2.4e-03|-1.427569e+02 -1.427574e+02| 0:0:18| spchol  1  1 
43|0.567|0.472|2.2e-11|1.4e-08|1.3e-03|-1.427570e+02 -1.427573e+02| 0:0:18| spchol  1  1 
44|0.569|0.472|2.7e-11|7.6e-09|6.9e-04|-1.427571e+02 -1.427572e+02| 0:0:19| spchol  1  1 
45|0.571|0.472|1.5e-10|4.1e-09|3.7e-04|-1.427571e+02 -1.427572e+02| 0:0:19| spchol  1  1 
46|0.574|0.472|2.2e-10|2.2e-09|2.1e-04|-1.427571e+02 -1.427572e+02| 0:0:20| spchol  1  1 
47|0.579|0.471|2.2e-11|1.2e-09|1.2e-04|-1.427572e+02 -1.427572e+02| 0:0:20| spchol  1  1 
48|0.591|0.471|2.7e-10|7.1e-10|7.0e-05|-1.427572e+02 -1.427572e+02| 0:0:21| spchol  1  1 
49|0.607|0.471|6.9e-11|4.2e-10|4.1e-05|-1.427572e+02 -1.427572e+02| 0:0:21| spchol  1  1 
50|0.626|0.471|1.9e-11|2.5e-10|2.4e-05|-1.427572e+02 -1.427572e+02| 0:0:21| spchol  1  1 
51|0.651|0.471|2.8e-11|1.5e-10|1.5e-05|-1.427572e+02 -1.427572e+02| 0:0:22| spchol  1  1 
52|0.682|0.471|5.0e-11|8.7e-11|8.6e-06|-1.427572e+02 -1.427572e+02| 0:0:22| spchol  1  1 
53|0.721|0.471|6.6e-11|5.1e-11|5.1e-06|-1.427572e+02 -1.427572e+02| 0:0:23| spchol  1  1 
54|0.770|0.471|8.5e-11|3.0e-11|3.0e-06|-1.427572e+02 -1.427572e+02| 0:0:23|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 54
 primal objective value = -1.42757166e+02
 dual   objective value = -1.42757166e+02
 gap := trace(XZ)       = 3.01e-06
 relative gap           = 1.05e-08
 actual relative gap    = 1.50e-09
 rel. primal infeas (scaled problem)   = 8.51e-11
 rel. dual     "        "       "      = 3.04e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.4e+04, 1.0e+07, 1.0e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 23.05  
 CPU time per iteration = 0.43  
 termination code       =  0
 DIMACS: 8.6e-11  0.0e+00  1.9e-10  0.0e+00  1.5e-09  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +136.386
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.441588e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.057|0.235|3.9e+02|1.0e+02|1.2e+09| 1.129466e+06 -6.131839e+04| 0:0:00| spchol  1  1 
 2|0.334|0.487|2.6e+02|5.1e+01|3.1e+08| 1.988078e+06 -9.938782e+04| 0:0:01| spchol  1  1 
 3|0.866|0.821|3.5e+01|9.2e+00|3.9e+07| 2.176620e+06 -1.085397e+05| 0:0:01| spchol  1  1 
 4|0.926|0.908|2.6e+00|8.6e-01|3.1e+06| 5.424189e+05 -9.350404e+04| 0:0:02| spchol  1  1 
 5|0.722|0.641|7.2e-01|3.1e-01|1.0e+06| 1.883118e+05 -5.731679e+04| 0:0:02| spchol  1  1 
 6|0.747|0.438|1.8e-01|1.8e-01|3.8e+05| 6.548075e+04 -3.699344e+04| 0:0:02| spchol  1  1 
 7|0.456|0.304|1.0e-01|1.2e-01|2.4e+05| 4.056545e+04 -2.695767e+04| 0:0:02| spchol  1  1 
 8|0.665|0.405|3.3e-02|7.3e-02|1.2e+05| 1.915219e+04 -1.698860e+04| 0:0:03| spchol  1  1 
 9|0.479|0.468|1.7e-02|4.3e-02|7.3e+04| 1.248403e+04 -9.601335e+03| 0:0:03| spchol  1  1 
10|0.684|0.403|5.5e-03|2.8e-02|3.9e+04| 6.479527e+03 -6.000430e+03| 0:0:03| spchol  1  1 
11|0.837|0.383|8.9e-04|1.8e-02|1.9e+04| 2.766727e+03 -3.823111e+03| 0:0:03| spchol  1  1 
12|0.884|0.325|1.0e-04|1.3e-02|1.0e+04| 1.147828e+03 -2.647410e+03| 0:0:04| spchol  1  1 
13|0.441|0.383|5.8e-05|7.8e-03|6.6e+03| 7.912486e+02 -1.680421e+03| 0:0:04| spchol  1  1 
14|0.512|0.210|2.8e-05|6.1e-03|5.0e+03| 4.699437e+02 -1.347777e+03| 0:0:04| spchol  1  1 
15|0.736|0.223|7.6e-06|4.8e-03|3.6e+03| 1.907272e+02 -1.065895e+03| 0:0:05| spchol  1  1 
16|0.739|0.301|2.1e-06|3.3e-03|2.4e+03| 6.671601e+01 -7.688132e+02| 0:0:05| spchol  1  1 
17|0.496|0.287|1.1e-06|2.4e-03|1.8e+03| 1.557343e+01 -5.815314e+02| 0:0:05| spchol  1  1 
18|0.634|0.235|4.4e-07|1.8e-03|1.3e+03|-6.967801e+01 -4.852363e+02| 0:0:05| spchol  1  1 
19|0.697|0.302|1.6e-07|1.3e-03|9.0e+02|-1.237314e+02 -3.929950e+02| 0:0:06| spchol  1  1 
20|0.983|0.286|7.8e-08|9.1e-04|6.4e+02|-1.554377e+02 -3.309866e+02| 0:0:06| spchol  1  1 
21|1.000|0.367|5.7e-08|5.8e-04|4.1e+02|-1.616761e+02 -2.732187e+02| 0:0:06| spchol  1  1 
22|1.000|0.370|3.5e-08|3.6e-04|2.6e+02|-1.656570e+02 -2.359225e+02| 0:0:07| spchol  1  1 
23|1.000|0.396|1.9e-08|2.2e-04|1.6e+02|-1.679797e+02 -2.103730e+02| 0:0:07| spchol  1  1 
24|1.000|0.304|1.4e-08|1.5e-04|1.1e+02|-1.686798e+02 -1.984840e+02| 0:0:07| spchol  1  1 
25|1.000|0.304|1.2e-08|1.1e-04|7.9e+01|-1.690687e+02 -1.901819e+02| 0:0:08| spchol  1  1 
26|1.000|0.310|8.6e-09|7.3e-05|5.6e+01|-1.694407e+02 -1.842211e+02| 0:0:08| spchol  1  1 
27|1.000|0.320|6.3e-09|5.0e-05|3.8e+01|-1.697381e+02 -1.799468e+02| 0:0:08| spchol  1  1 
28|1.000|0.336|4.1e-09|3.3e-05|2.6e+01|-1.699978e+02 -1.768542e+02| 0:0:09| spchol  1  1 
29|1.000|0.360|2.5e-09|2.1e-05|1.6e+01|-1.701995e+02 -1.746215e+02| 0:0:09| spchol  1  1 
30|0.977|0.385|1.3e-09|1.3e-05|1.0e+01|-1.703425e+02 -1.730635e+02| 0:0:10| spchol  1  1 
31|0.928|0.393|7.0e-10|7.9e-06|6.0e+00|-1.704170e+02 -1.720702e+02| 0:0:10| spchol  1  1 
32|0.967|0.355|3.7e-10|5.1e-06|3.8e+00|-1.704559e+02 -1.715206e+02| 0:0:10| spchol  1  1 
33|1.000|0.375|2.0e-10|3.2e-06|2.4e+00|-1.704761e+02 -1.711417e+02| 0:0:11| spchol  1  1 
34|0.963|0.385|1.1e-10|2.0e-06|1.5e+00|-1.704869e+02 -1.708966e+02| 0:0:11| spchol  1  1 
35|1.000|0.306|8.1e-11|1.4e-06|1.0e+00|-1.704902e+02 -1.707766e+02| 0:0:11| spchol  1  1 
36|1.000|0.286|6.6e-11|9.7e-07|7.4e-01|-1.704918e+02 -1.706983e+02| 0:0:12| spchol  1  1 
37|1.000|0.324|4.9e-11|6.6e-07|5.1e-01|-1.704936e+02 -1.706348e+02| 0:0:12| spchol  1  1 
38|1.000|0.330|6.8e-11|3.0e-06|3.5e-01|-1.704954e+02 -1.705907e+02| 0:0:12| spchol  1  1 
39|1.000|0.890|2.4e-11|2.0e-06|5.5e-02|-1.704966e+02 -1.705105e+02| 0:0:13| spchol  1  1 
40|0.627|0.926|1.2e-11|3.2e-07|1.2e-02|-1.704978e+02 -1.705003e+02| 0:0:13| spchol  1  1 
41|0.573|0.472|6.5e-12|7.2e-08|6.5e-03|-1.704984e+02 -1.704998e+02| 0:0:13| spchol  1  1 
42|0.575|0.472|2.7e-11|3.8e-08|3.5e-03|-1.704988e+02 -1.704995e+02| 0:0:14| spchol  1  1 
43|0.577|0.472|2.1e-12|2.1e-08|1.9e-03|-1.704989e+02 -1.704993e+02| 0:0:14| spchol  1  1 
44|0.579|0.472|6.2e-11|1.1e-08|1.0e-03|-1.704990e+02 -1.704993e+02| 0:0:14| spchol  1  1 
45|0.581|0.472|1.3e-10|6.0e-09|5.4e-04|-1.704991e+02 -1.704992e+02| 0:0:15| spchol  1  1 
46|0.583|0.472|1.5e-11|3.2e-09|2.9e-04|-1.704991e+02 -1.704992e+02| 0:0:15| spchol  1  1 
47|0.586|0.471|5.9e-12|1.7e-09|1.6e-04|-1.704991e+02 -1.704991e+02| 0:0:15| spchol  1  1 
48|0.591|0.471|1.5e-10|9.5e-10|8.8e-05|-1.704991e+02 -1.704991e+02| 0:0:16| spchol  1  1 
49|0.595|0.471|3.4e-10|5.2e-10|4.9e-05|-1.704991e+02 -1.704991e+02| 0:0:16| spchol  1  1 
50|0.602|0.471|2.1e-10|2.9e-10|2.9e-05|-1.704991e+02 -1.704991e+02| 0:0:17| spchol  1  1 
51|0.623|0.471|4.2e-11|1.7e-10|1.7e-05|-1.704991e+02 -1.704991e+02| 0:0:17| spchol  2  1 
52|0.648|0.471|1.9e-10|1.0e-10|1.0e-05|-1.704991e+02 -1.704991e+02| 0:0:17| spchol  2  1 
53|0.678|0.471|1.6e-11|6.1e-11|6.1e-06|-1.704991e+02 -1.704991e+02| 0:0:18| spchol  2  1 
54|0.716|0.471|4.9e-11|3.6e-11|3.6e-06|-1.704991e+02 -1.704991e+02| 0:0:18|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 54
 primal objective value = -1.70499126e+02
 dual   objective value = -1.70499127e+02
 gap := trace(XZ)       = 3.59e-06
 relative gap           = 1.05e-08
 actual relative gap    = 1.77e-09
 rel. primal infeas (scaled problem)   = 4.94e-11
 rel. dual     "        "       "      = 3.58e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 2.9e+04, 1.2e+07, 1.2e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 17.96  
 CPU time per iteration = 0.33  
 termination code       =  0
 DIMACS: 5.0e-11  0.0e+00  2.0e-10  0.0e+00  1.8e-09  1.0e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +167.378
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.9e+09| 7.447588e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.059|0.239|3.9e+02|9.9e+01|1.2e+09| 1.133991e+06 -6.154875e+04| 0:0:01| spchol  1  1 
 2|0.351|0.494|2.6e+02|5.0e+01|3.1e+08| 2.033991e+06 -1.000513e+05| 0:0:01| spchol  1  1 
 3|0.873|0.825|3.2e+01|8.8e+00|3.6e+07| 2.167283e+06 -1.086874e+05| 0:0:01| spchol  1  1 
 4|0.917|0.907|2.7e+00|8.2e-01|3.2e+06| 5.378874e+05 -9.252929e+04| 0:0:02| spchol  1  1 
 5|0.727|0.655|7.3e-01|2.9e-01|1.0e+06| 1.841946e+05 -5.621698e+04| 0:0:02| spchol  1  1 
 6|0.710|0.402|2.1e-01|1.7e-01|4.1e+05| 7.004235e+04 -3.808198e+04| 0:0:02| spchol  1  1 
 7|0.488|0.322|1.1e-01|1.2e-01|2.5e+05| 4.162680e+04 -2.720023e+04| 0:0:02| spchol  1  1 
 8|0.677|0.456|3.5e-02|6.4e-02|1.1e+05| 1.929601e+04 -1.587832e+04| 0:0:02| spchol  1  1 
 9|0.460|0.432|1.9e-02|4.1e-02|7.3e+04| 1.273510e+04 -9.504856e+03| 0:0:02| spchol  1  1 
10|0.686|0.376|5.9e-03|2.8e-02|4.0e+04| 6.516895e+03 -6.176126e+03| 0:0:03| spchol  1  1 
11|0.836|0.373|9.7e-04|1.9e-02|1.9e+04| 2.753973e+03 -3.990344e+03| 0:0:03| spchol  1  1 
12|0.932|0.348|6.6e-05|1.2e-02|1.0e+04| 1.059933e+03 -2.674606e+03| 0:0:03| spchol  1  1 
13|0.411|0.391|3.9e-05|7.5e-03|6.6e+03| 7.537279e+02 -1.677129e+03| 0:0:03| spchol  1  1 
14|0.527|0.202|1.9e-05|6.0e-03|5.0e+03| 4.340129e+02 -1.358248e+03| 0:0:03| spchol  1  1 
15|0.719|0.224|5.3e-06|4.7e-03|3.6e+03| 1.777073e+02 -1.074702e+03| 0:0:04| spchol  1  1 
16|0.499|0.294|2.7e-06|3.3e-03|2.6e+03| 9.192740e+01 -7.885421e+02| 0:0:04| spchol  1  1 
17|0.569|0.223|1.2e-06|2.6e-03|2.0e+03|-3.464701e+00 -6.482663e+02| 0:0:04| spchol  1  1 
18|0.605|0.233|5.2e-07|2.0e-03|1.5e+03|-9.033031e+01 -5.464202e+02| 0:0:04| spchol  1  1 
19|0.687|0.316|1.9e-07|1.3e-03|1.0e+03|-1.473120e+02 -4.399558e+02| 0:0:04| spchol  1  1 
20|0.948|0.284|8.0e-08|9.6e-04|7.0e+02|-1.806926e+02 -3.731090e+02| 0:0:04| spchol  1  1 
21|1.000|0.357|6.0e-08|6.2e-04|4.6e+02|-1.882432e+02 -3.119081e+02| 0:0:05| spchol  1  1 
22|1.000|0.366|3.7e-08|3.9e-04|3.0e+02|-1.927167e+02 -2.711621e+02| 0:0:05| spchol  1  1 
23|1.000|0.340|2.6e-08|2.6e-04|2.0e+02|-1.947150e+02 -2.469143e+02| 0:0:05| spchol  1  1 
24|1.000|0.356|1.6e-08|1.7e-04|1.3e+02|-1.961929e+02 -2.299459e+02| 0:0:05| spchol  1  1 
25|1.000|0.360|9.5e-09|1.1e-04|8.2e+01|-1.970561e+02 -2.187562e+02| 0:0:05| spchol  1  1 
26|1.000|0.300|7.3e-09|7.5e-05|5.8e+01|-1.973721e+02 -2.127693e+02| 0:0:05| spchol  1  1 
27|1.000|0.304|5.8e-09|5.2e-05|4.1e+01|-1.975648e+02 -2.084925e+02| 0:0:06| spchol  1  1 
28|1.000|0.305|4.5e-09|3.6e-05|2.9e+01|-1.977482e+02 -2.054771e+02| 0:0:06| spchol  1  1 
29|1.000|0.328|3.2e-09|2.4e-05|2.0e+01|-1.979249e+02 -2.031984e+02| 0:0:06| spchol  1  1 
30|1.000|0.350|1.9e-09|1.6e-05|1.3e+01|-1.980881e+02 -2.015400e+02| 0:0:06| spchol  1  1 
31|0.956|0.398|1.0e-09|9.5e-06|7.8e+00|-1.982062e+02 -2.002917e+02| 0:0:06| spchol  1  1 
32|0.861|0.395|5.5e-10|5.8e-06|4.7e+00|-1.982679e+02 -1.995313e+02| 0:0:07| spchol  1  1 
33|0.882|0.355|2.9e-10|3.7e-06|3.0e+00|-1.983002e+02 -1.991134e+02| 0:0:07| spchol  1  1 
34|0.912|0.349|1.6e-10|2.4e-06|1.9e+00|-1.983172e+02 -1.988454e+02| 0:0:07| spchol  1  1 
35|0.921|0.375|8.4e-11|1.5e-06|1.2e+00|-1.983262e+02 -1.986563e+02| 0:0:07| spchol  1  1 
36|1.000|0.335|4.8e-11|1.0e-06|7.8e-01|-1.983307e+02 -1.985502e+02| 0:0:07| spchol  1  1 
37|1.000|0.310|3.7e-11|6.9e-07|5.5e-01|-1.983319e+02 -1.984846e+02| 0:0:07| spchol  1  1 
38|1.000|0.292|3.2e-11|3.2e-06|4.0e-01|-1.983328e+02 -1.984418e+02| 0:0:08| spchol  1  1 
39|1.000|0.892|2.3e-11|2.3e-06|6.2e-02|-1.983335e+02 -1.983490e+02| 0:0:08| spchol  1  1 
40|0.658|0.928|1.2e-11|3.6e-07|1.4e-02|-1.983348e+02 -1.983376e+02| 0:0:08| spchol  1  1 
41|0.573|0.472|7.4e-12|7.9e-08|7.3e-03|-1.983355e+02 -1.983371e+02| 0:0:08| spchol  1  1 
42|0.575|0.472|7.1e-12|4.2e-08|3.9e-03|-1.983359e+02 -1.983367e+02| 0:0:08| spchol  1  1 
43|0.577|0.472|3.9e-12|2.3e-08|2.1e-03|-1.983361e+02 -1.983365e+02| 0:0:09| spchol  1  1 
44|0.579|0.472|3.3e-12|1.2e-08|1.1e-03|-1.983362e+02 -1.983364e+02| 0:0:09| spchol  1  1 
45|0.581|0.471|3.6e-11|6.5e-09|6.0e-04|-1.983362e+02 -1.983364e+02| 0:0:09| spchol  1  1 
46|0.583|0.471|5.2e-11|3.5e-09|3.3e-04|-1.983363e+02 -1.983363e+02| 0:0:09| spchol  1  1 
47|0.586|0.471|2.8e-11|1.9e-09|1.8e-04|-1.983363e+02 -1.983363e+02| 0:0:09| spchol  1  1 
48|0.590|0.471|8.1e-12|1.0e-09|9.9e-05|-1.983363e+02 -1.983363e+02| 0:0:09| spchol  1  1 
49|0.597|0.471|5.8e-11|5.8e-10|5.5e-05|-1.983363e+02 -1.983363e+02| 0:0:10| spchol  1  1 
50|0.606|0.471|8.0e-11|3.2e-10|3.3e-05|-1.983363e+02 -1.983363e+02| 0:0:10| spchol  1  1 
51|0.627|0.471|5.9e-11|1.9e-10|1.9e-05|-1.983363e+02 -1.983363e+02| 0:0:10| spchol  1  1 
52|0.653|0.471|2.4e-11|1.1e-10|1.1e-05|-1.983363e+02 -1.983363e+02| 0:0:10| spchol  1  1 
53|0.684|0.471|6.9e-11|6.7e-11|6.8e-06|-1.983363e+02 -1.983363e+02| 0:0:10| spchol  1  1 
54|0.723|0.471|2.8e-11|3.9e-11|4.0e-06|-1.983363e+02 -1.983363e+02| 0:0:10|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 54
 primal objective value = -1.98336296e+02
 dual   objective value = -1.98336297e+02
 gap := trace(XZ)       = 4.01e-06
 relative gap           = 1.01e-08
 actual relative gap    = 1.70e-09
 rel. primal infeas (scaled problem)   = 2.76e-11
 rel. dual     "        "       "      = 3.94e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 2.9e+04, 1.3e+07, 1.3e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.1e+02
 Total CPU time (secs)  = 10.44  
 CPU time per iteration = 0.19  
 termination code       =  0
 DIMACS: 2.8e-11  0.0e+00  1.9e-10  0.0e+00  1.7e-09  1.0e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +198.965
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.9e+09| 7.453588e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.061|0.243|3.9e+02|9.7e+01|1.2e+09| 1.138935e+06 -6.183689e+04| 0:0:01| spchol  1  1 
 2|0.371|0.501|2.5e+02|4.8e+01|3.0e+08| 2.088983e+06 -1.007869e+05| 0:0:02| spchol  1  1 
 3|0.883|0.830|2.9e+01|8.2e+00|3.4e+07| 2.152550e+06 -1.087599e+05| 0:0:03| spchol  1  1 
 4|0.906|0.905|2.7e+00|7.9e-01|3.2e+06| 5.321648e+05 -9.107854e+04| 0:0:03| spchol  1  1 
 5|0.709|0.658|8.0e-01|2.7e-01|1.1e+06| 1.909039e+05 -5.536399e+04| 0:0:04| spchol  1  1 
 6|0.670|0.375|2.6e-01|1.7e-01|4.7e+05| 7.867510e+04 -3.905750e+04| 0:0:04| spchol  1  1 
 7|0.488|0.320|1.3e-01|1.2e-01|2.8e+05| 4.656155e+04 -2.811441e+04| 0:0:05| spchol  1  1 
 8|0.698|0.424|4.1e-02|6.7e-02|1.2e+05| 2.046214e+04 -1.727772e+04| 0:0:06| spchol  1  1 
 9|0.515|0.509|2.0e-02|3.7e-02|7.2e+04| 1.276282e+04 -9.091739e+03| 0:0:06| spchol  1  1 
10|0.643|0.389|7.0e-03|2.6e-02|4.0e+04| 6.871134e+03 -5.805404e+03| 0:0:07| spchol  1  1 
11|0.828|0.359|1.2e-03|1.8e-02|1.9e+04| 2.781622e+03 -3.833320e+03| 0:0:07| spchol  1  1 
12|0.929|0.336|8.6e-05|1.2e-02|1.0e+04| 1.014555e+03 -2.616636e+03| 0:0:08| spchol  1  1 
13|0.408|0.398|5.1e-05|7.2e-03|6.6e+03| 7.184223e+02 -1.624696e+03| 0:0:09| spchol  1  1 
14|0.559|0.202|2.3e-05|5.7e-03|5.0e+03| 3.866830e+02 -1.318169e+03| 0:0:09| spchol  1  1 
15|0.627|0.239|8.5e-06|4.4e-03|3.6e+03| 1.772668e+02 -1.028686e+03| 0:0:10| spchol  1  1 
16|0.490|0.256|4.4e-06|3.3e-03|2.7e+03| 7.431105e+01 -8.019057e+02| 0:0:10| spchol  1  1 
17|0.536|0.222|2.1e-06|2.5e-03|2.1e+03|-3.783111e+01 -6.730756e+02| 0:0:11| spchol  1  1 
18|0.569|0.226|9.1e-07|2.0e-03|1.6e+03|-1.183277e+02 -5.761313e+02| 0:0:12| spchol  1  1 
19|0.636|0.294|3.4e-07|1.4e-03|1.1e+03|-1.701637e+02 -4.768475e+02| 0:0:12| spchol  1  1 
20|0.818|0.266|1.1e-07|1.0e-03|7.8e+02|-2.017859e+02 -4.121827e+02| 0:0:13| spchol  1  1 
21|1.000|0.316|7.1e-08|6.9e-04|5.4e+02|-2.143083e+02 -3.548664e+02| 0:0:13| spchol  1  1 
22|1.000|0.360|4.7e-08|4.4e-04|3.5e+02|-2.192651e+02 -3.096269e+02| 0:0:14| spchol  1  1 
23|1.000|0.331|3.5e-08|3.0e-04|2.4e+02|-2.217087e+02 -2.827709e+02| 0:0:15| spchol  1  1 
24|1.000|0.347|2.3e-08|1.9e-04|1.6e+02|-2.235959e+02 -2.637035e+02| 0:0:15| spchol  1  1 
25|1.000|0.363|1.3e-08|1.2e-04|1.0e+02|-2.248386e+02 -2.504956e+02| 0:0:16| spchol  1  1 
26|1.000|0.367|7.6e-09|7.8e-05|6.4e+01|-2.255864e+02 -2.418600e+02| 0:0:16| spchol  1  1 
27|1.000|0.368|4.3e-09|4.9e-05|4.0e+01|-2.259907e+02 -2.363057e+02| 0:0:17| spchol  1  1 
28|1.000|0.359|2.5e-09|3.2e-05|2.6e+01|-2.262055e+02 -2.328421e+02| 0:0:18| spchol  1  1 
29|1.000|0.348|1.5e-09|2.1e-05|1.7e+01|-2.263205e+02 -2.306675e+02| 0:0:18| spchol  1  1 
30|1.000|0.345|9.8e-10|1.4e-05|1.1e+01|-2.263867e+02 -2.292532e+02| 0:0:19| spchol  1  1 
31|1.000|0.343|6.2e-10|8.9e-06|7.2e+00|-2.264283e+02 -2.283228e+02| 0:0:20| spchol  1  1 
32|1.000|0.352|3.8e-10|5.8e-06|4.7e+00|-2.264557e+02 -2.276901e+02| 0:0:20| spchol  1  1 
33|1.000|0.360|2.2e-10|3.7e-06|3.0e+00|-2.264741e+02 -2.272673e+02| 0:0:21| spchol  1  1 
34|1.000|0.375|1.2e-10|2.3e-06|1.9e+00|-2.264857e+02 -2.269827e+02| 0:0:21| spchol  1  1 
35|1.000|0.377|6.7e-11|1.4e-06|1.2e+00|-2.264923e+02 -2.268023e+02| 0:0:22| spchol  1  1 
36|1.000|0.377|3.7e-11|9.0e-07|7.2e-01|-2.264958e+02 -2.266893e+02| 0:0:23| spchol  1  1 
37|1.000|0.360|2.1e-11|5.7e-07|4.6e-01|-2.264976e+02 -2.266215e+02| 0:0:23| spchol  1  1 
38|1.000|0.353|1.3e-11|2.6e-06|3.0e-01|-2.264985e+02 -2.265789e+02| 0:0:24| spchol  1  1 
39|1.000|0.918|8.6e-12|1.7e-06|3.2e-02|-2.264991e+02 -2.265069e+02| 0:0:25| spchol  1  1 
40|0.553|0.939|4.5e-12|1.8e-07|5.1e-03|-2.264995e+02 -2.265005e+02| 0:0:26| spchol  1  1 
41|0.585|0.472|2.4e-12|2.9e-08|2.7e-03|-2.264998e+02 -2.265003e+02| 0:0:26| spchol  1  1 
42|0.586|0.471|1.3e-12|1.5e-08|1.4e-03|-2.264999e+02 -2.265002e+02| 0:0:27| spchol  1  1 
43|0.588|0.471|7.1e-13|8.3e-09|7.8e-04|-2.264999e+02 -2.265001e+02| 0:0:28| spchol  1  1 
44|0.591|0.471|8.3e-13|4.5e-09|4.2e-04|-2.265000e+02 -2.265001e+02| 0:0:28| spchol  1  1 
45|0.593|0.471|3.2e-12|2.4e-09|2.3e-04|-2.265000e+02 -2.265000e+02| 0:0:29| spchol  1  1 
46|0.596|0.471|7.1e-13|1.3e-09|1.2e-04|-2.265000e+02 -2.265000e+02| 0:0:29| spchol  1  1 
47|0.600|0.471|9.0e-13|7.1e-10|6.7e-05|-2.265000e+02 -2.265000e+02| 0:0:30| spchol  1  1 
48|0.605|0.471|8.4e-14|3.9e-10|3.7e-05|-2.265000e+02 -2.265000e+02| 0:0:31| spchol  1  1 
49|0.613|0.471|7.3e-13|2.2e-10|2.1e-05|-2.265000e+02 -2.265000e+02| 0:0:31| spchol  1  1 
50|0.627|0.471|4.4e-13|1.2e-10|1.2e-05|-2.265000e+02 -2.265000e+02| 0:0:32| spchol  1  1 
51|0.653|0.471|1.9e-12|7.3e-11|7.3e-06|-2.265000e+02 -2.265000e+02| 0:0:33| spchol  1  1 
52|0.684|0.471|5.3e-12|4.3e-11|4.3e-06|-2.265000e+02 -2.265000e+02| 0:0:33|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 52
 primal objective value = -2.26500019e+02
 dual   objective value = -2.26500020e+02
 gap := trace(XZ)       = 4.33e-06
 relative gap           = 9.54e-09
 actual relative gap    = 1.77e-09
 rel. primal infeas (scaled problem)   = 5.26e-12
 rel. dual     "        "       "      = 4.31e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 2.6e+04, 1.2e+07, 1.2e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.1e+02
 Total CPU time (secs)  = 33.18  
 CPU time per iteration = 0.64  
 termination code       =  0
 DIMACS: 5.3e-12  0.0e+00  1.9e-10  0.0e+00  1.8e-09  9.5e-09
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +231.379
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.4e+02|6.8e+09| 7.417126e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.053|0.225|4.0e+02|1.1e+02|1.3e+09| 1.117920e+06 -6.093904e+04| 0:0:01| spchol  1  1 
 2|0.295|0.467|2.8e+02|5.6e+01|3.3e+08| 1.878981e+06 -9.769146e+04| 0:0:02| spchol  1  1 
 3|0.850|0.820|4.2e+01|1.0e+01|4.3e+07| 2.156954e+06 -1.073325e+05| 0:0:03| spchol  1  1 
 4|0.900|0.908|4.2e+00|9.4e-01|4.3e+06| 6.074246e+05 -9.450268e+04| 0:0:03| spchol  1  1 
 5|0.691|0.593|1.3e+00|3.8e-01|1.6e+06| 2.361693e+05 -6.787132e+04| 0:0:04| spchol  1  1 
 6|0.790|0.485|2.7e-01|2.0e-01|4.8e+05| 7.554786e+04 -4.361923e+04| 0:0:04| spchol  1  1 
 7|0.450|0.323|1.5e-01|1.4e-01|3.0e+05| 4.675181e+04 -3.110479e+04| 0:0:05| spchol  1  1 
 8|0.582|0.349|6.2e-02|8.8e-02|1.6e+05| 2.460011e+04 -2.133619e+04| 0:0:06| spchol  1  1 
 9|0.670|0.376|2.0e-02|6.0e-02|9.1e+04| 1.216524e+04 -1.396998e+04| 0:0:06| spchol  1  1 
10|0.656|0.505|7.0e-03|3.2e-02|4.8e+04| 7.049163e+03 -7.360440e+03| 0:0:07| spchol  1  1 
11|0.763|0.367|1.7e-03|2.2e-02|2.6e+04| 3.669625e+03 -4.834640e+03| 0:0:08| spchol  1  1 
12|0.554|0.306|7.4e-04|1.5e-02|1.7e+04| 2.405737e+03 -3.447248e+03| 0:0:08| spchol  1  1 
13|0.313|0.172|5.1e-04|1.6e-02|1.5e+04| 1.907337e+03 -2.894726e+03| 0:0:09| spchol  1  1 
14|0.497|0.465|2.6e-04|8.9e-03|8.4e+03| 1.309260e+03 -1.625942e+03| 0:0:10| spchol  1  1 
15|0.368|0.180|1.6e-04|9.6e-03|6.8e+03| 9.608742e+02 -1.358320e+03| 0:0:10| spchol  1  1 
16|0.824|0.409|2.9e-05|5.7e-03|3.4e+03| 3.919513e+02 -8.400862e+02| 0:0:11| spchol  1  1 
17|0.569|0.302|1.2e-05|4.0e-03|2.2e+03| 2.059465e+02 -6.039519e+02| 0:0:11| spchol  1  1 
18|0.378|0.271|7.7e-06|2.9e-03|1.7e+03| 1.295821e+02 -4.509520e+02| 0:0:12| spchol  1  1 
19|0.427|0.163|4.4e-06|3.3e-03|1.4e+03| 7.966790e+01 -3.822351e+02| 0:0:13| spchol  1  1 
20|0.533|0.409|2.1e-06|2.0e-03|8.2e+02| 4.046591e+01 -2.368417e+02| 0:0:13| spchol  1  1 
21|0.587|0.231|8.6e-07|1.5e-03|6.0e+02| 6.119539e+00 -1.915167e+02| 0:0:14| spchol  1  1 
22|0.702|0.236|2.9e-07|1.1e-03|4.4e+02|-3.040270e+01 -1.614417e+02| 0:0:15| spchol  1  1 
23|1.000|0.319|8.2e-08|7.8e-04|2.9e+02|-5.280975e+01 -1.301776e+02| 0:0:15| spchol  1  1 
24|1.000|0.411|5.0e-08|4.6e-04|1.7e+02|-5.688866e+01 -1.022919e+02| 0:0:16| spchol  1  1 
25|1.000|0.390|2.8e-08|2.8e-04|1.0e+02|-5.883239e+01 -8.646456e+01| 0:0:17| spchol  1  1 
26|1.000|0.352|1.7e-08|1.8e-04|6.8e+01|-5.963733e+01 -7.762794e+01| 0:0:17| spchol  1  1 
27|1.000|0.298|1.4e-08|1.3e-04|4.9e+01|-5.989577e+01 -7.275400e+01| 0:0:18| spchol  1  1 
28|1.000|0.310|1.0e-08|8.8e-05|3.4e+01|-6.015624e+01 -6.916736e+01| 0:0:19| spchol  1  1 
29|1.000|0.358|6.4e-09|5.7e-05|2.2e+01|-6.042750e+01 -6.626746e+01| 0:0:19| spchol  1  1 
30|0.992|0.383|3.4e-09|3.5e-05|1.4e+01|-6.063501e+01 -6.423711e+01| 0:0:20| spchol  1  1 
31|1.000|0.357|2.1e-09|2.2e-05|8.7e+00|-6.072583e+01 -6.305891e+01| 0:0:20| spchol  1  1 
32|1.000|0.352|1.2e-09|1.5e-05|5.6e+00|-6.078432e+01 -6.230030e+01| 0:0:21| spchol  1  1 
33|0.933|0.409|6.6e-10|8.6e-06|3.3e+00|-6.082163e+01 -6.172182e+01| 0:0:22| spchol  1  1 
34|1.000|0.348|3.7e-10|5.6e-06|2.1e+00|-6.084093e+01 -6.142780e+01| 0:0:22| spchol  1  1 
35|1.000|0.348|2.3e-10|3.7e-06|1.4e+00|-6.085015e+01 -6.123465e+01| 0:0:23| spchol  1  1 
36|1.000|0.337|1.7e-10|2.4e-06|9.4e-01|-6.085437e+01 -6.111196e+01| 0:0:23| spchol  1  1 
37|1.000|0.310|1.3e-10|1.7e-06|6.5e-01|-6.085735e+01 -6.103663e+01| 0:0:24| spchol  1  1 
38|1.000|0.353|1.1e-10|4.0e-06|4.3e-01|-6.085979e+01 -6.097685e+01| 0:0:24| spchol  1  1 
39|1.000|0.934|8.3e-11|2.6e-06|4.9e-02|-6.086190e+01 -6.087369e+01| 0:0:25| spchol  1  1 
40|0.581|0.939|4.8e-11|3.0e-07|1.3e-02|-6.086330e+01 -6.086568e+01| 0:0:26| spchol  1  1 
41|0.560|0.472|6.8e-11|7.7e-08|6.7e-03|-6.086404e+01 -6.086535e+01| 0:0:26| spchol  1  1 
42|0.562|0.472|4.2e-10|4.1e-08|3.6e-03|-6.086443e+01 -6.086516e+01| 0:0:27| spchol  1  1 
43|0.564|0.472|1.4e-09|2.2e-08|2.0e-03|-6.086463e+01 -6.086504e+01| 0:0:27| spchol  2  2 
44|0.567|0.472|6.0e-10|1.2e-08|1.1e-03|-6.086474e+01 -6.086497e+01| 0:0:28| spchol  1  2 
45|0.573|0.471|2.6e-10|6.7e-09|6.5e-04|-6.086480e+01 -6.086492e+01| 0:0:29| spchol  1  1 
46|0.587|0.471|5.5e-10|4.0e-09|3.8e-04|-6.086483e+01 -6.086490e+01| 0:0:29| spchol  2  2 
47|0.605|0.471|2.2e-10|2.3e-09|2.3e-04|-6.086485e+01 -6.086488e+01| 0:0:30| spchol  2  1 
48|0.624|0.471|4.7e-10|1.4e-09|1.3e-04|-6.086486e+01 -6.086488e+01| 0:0:31| spchol  2  2 
49|0.629|0.471|1.7e-10|8.2e-10|8.0e-05|-6.086486e+01 -6.086487e+01| 0:0:32| spchol  2  2 
50|0.657|0.471|6.0e-11|4.9e-10|4.8e-05|-6.086486e+01 -6.086487e+01| 0:0:32| spchol  2  2 
51|0.692|0.471|1.8e-11|2.9e-10|2.8e-05|-6.086486e+01 -6.086487e+01| 0:0:33| spchol  2  2 
52|0.735|0.471|5.0e-12|1.7e-10|1.7e-05|-6.086486e+01 -6.086487e+01| 0:0:34| spchol  2  2 
53|0.789|0.471|1.4e-12|1.0e-10|1.0e-05|-6.086486e+01 -6.086487e+01| 0:0:34| spchol  2  1 
54|0.860|0.471|2.6e-11|6.2e-11|5.9e-06|-6.086486e+01 -6.086487e+01| 0:0:35| spchol  2  2 
55|0.956|0.471|1.7e-12|3.7e-11|3.5e-06|-6.086486e+01 -6.086487e+01| 0:0:35| spchol  1  2 
56|1.000|0.471|1.2e-12|2.2e-11|2.1e-06|-6.086486e+01 -6.086487e+01| 0:0:36| spchol  2  2 
57|1.000|0.471|1.3e-12|1.3e-11|1.3e-06|-6.086486e+01 -6.086487e+01| 0:0:37|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 57
 primal objective value = -6.08648649e+01
 dual   objective value = -6.08648650e+01
 gap := trace(XZ)       = 1.30e-06
 relative gap           = 1.06e-08
 actual relative gap    = 1.13e-09
 rel. primal infeas (scaled problem)   = 1.35e-12
 rel. dual     "        "       "      = 1.31e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.6e+04, 6.4e+06, 6.4e+06
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 36.82  
 CPU time per iteration = 0.65  
 termination code       =  0
 DIMACS: 1.4e-12  0.0e+00  1.3e-10  0.0e+00  1.1e-09  1.1e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +42.7031
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.423126e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.054|0.227|4.0e+02|1.0e+02|1.3e+09| 1.120233e+06 -6.094508e+04| 0:0:01| spchol  1  1 
 2|0.300|0.471|2.8e+02|5.5e+01|3.2e+08| 1.895622e+06 -9.790740e+04| 0:0:02| spchol  1  1 
 3|0.852|0.819|4.1e+01|1.0e+01|4.3e+07| 2.165917e+06 -1.075867e+05| 0:0:03| spchol  1  1 
 4|0.908|0.908|3.8e+00|9.3e-01|4.0e+06| 5.951958e+05 -9.445736e+04| 0:0:03| spchol  1  1 
 5|0.693|0.597|1.2e+00|3.8e-01|1.5e+06| 2.281696e+05 -6.599536e+04| 0:0:04| spchol  1  1 
 6|0.786|0.480|2.5e-01|2.0e-01|4.6e+05| 7.342152e+04 -4.210106e+04| 0:0:04| spchol  1  1 
 7|0.443|0.313|1.4e-01|1.4e-01|2.9e+05| 4.593115e+04 -3.037126e+04| 0:0:05| spchol  1  1 
 8|0.580|0.353|5.8e-02|8.8e-02|1.6e+05| 2.438804e+04 -2.072040e+04| 0:0:06| spchol  1  1 
 9|0.666|0.372|1.9e-02|6.0e-02|8.9e+04| 1.221738e+04 -1.363466e+04| 0:0:06| spchol  1  1 
10|0.664|0.495|6.5e-03|3.3e-02|4.6e+04| 7.043604e+03 -7.311822e+03| 0:0:07| spchol  1  1 
11|0.793|0.390|1.3e-03|2.1e-02|2.4e+04| 3.500343e+03 -4.635028e+03| 0:0:08| spchol  1  1 
12|0.549|0.318|6.1e-04|1.5e-02|1.6e+04| 2.279196e+03 -3.249739e+03| 0:0:08| spchol  1  1 
13|0.338|0.169|4.0e-04|1.6e-02|1.3e+04| 1.743498e+03 -2.736427e+03| 0:0:09| spchol  1  1 
14|0.510|0.453|2.0e-04|8.7e-03|7.5e+03| 1.163870e+03 -1.564793e+03| 0:0:09| spchol  1  1 
15|0.393|0.211|1.2e-04|6.9e-03|5.8e+03| 8.250753e+02 -1.261088e+03| 0:0:10| spchol  1  1 
16|0.750|0.249|3.0e-05|5.2e-03|3.6e+03| 3.362501e+02 -9.686495e+02| 0:0:11| spchol  1  1 
17|0.619|0.280|1.1e-05|3.7e-03|2.5e+03| 1.606138e+02 -7.140827e+02| 0:0:11| spchol  1  1 
18|0.423|0.275|6.6e-06|2.7e-03|1.8e+03| 1.039113e+02 -5.293748e+02| 0:0:12| spchol  1  1 
19|0.531|0.188|3.1e-06|2.9e-03|1.4e+03| 5.780604e+01 -4.381798e+02| 0:0:12| spchol  1  1 
20|0.769|0.467|7.2e-07|1.5e-03|7.6e+02| 3.320898e+00 -2.561131e+02| 0:0:13| spchol  1  1 
21|0.817|0.255|1.9e-07|1.1e-03|5.5e+02|-6.119556e+01 -2.163786e+02| 0:0:14| spchol  1  1 
22|1.000|0.389|7.4e-08|7.0e-04|3.3e+02|-7.955192e+01 -1.678626e+02| 0:0:14| spchol  1  1 
23|1.000|0.393|4.7e-08|4.2e-04|2.0e+02|-8.394990e+01 -1.373094e+02| 0:0:15| spchol  1  1 
24|1.000|0.395|2.6e-08|2.6e-04|1.2e+02|-8.615158e+01 -1.183513e+02| 0:0:15| spchol  1  1 
25|1.000|0.337|1.7e-08|1.7e-04|8.1e+01|-8.699757e+01 -1.084676e+02| 0:0:16| spchol  1  1 
26|1.000|0.305|1.3e-08|1.2e-04|5.8e+01|-8.730578e+01 -1.024888e+02| 0:0:17| spchol  1  1 
27|1.000|0.311|1.0e-08|8.1e-05|4.0e+01|-8.761348e+01 -9.822668e+01| 0:0:17| spchol  1  1 
28|1.000|0.366|6.3e-09|5.2e-05|2.6e+01|-8.792104e+01 -9.472531e+01| 0:0:18| spchol  1  1 
29|1.000|0.368|3.4e-09|3.3e-05|1.6e+01|-8.815028e+01 -9.245273e+01| 0:0:18| spchol  1  1 
30|1.000|0.373|2.0e-09|2.0e-05|1.0e+01|-8.826584e+01 -9.098078e+01| 0:0:19| spchol  1  1 
31|1.000|0.330|1.3e-09|1.4e-05|6.8e+00|-8.832068e+01 -9.015396e+01| 0:0:20| spchol  1  1 
32|0.963|0.398|7.2e-10|8.2e-06|4.1e+00|-8.836895e+01 -8.947676e+01| 0:0:20| spchol  1  1 
33|0.981|0.366|3.9e-10|5.2e-06|2.6e+00|-8.839436e+01 -8.909614e+01| 0:0:21| spchol  1  1 
34|1.000|0.353|2.5e-10|3.4e-06|1.7e+00|-8.840567e+01 -8.886227e+01| 0:0:21| spchol  1  1 
35|1.000|0.326|1.7e-10|2.3e-06|1.1e+00|-8.841179e+01 -8.872133e+01| 0:0:22| spchol  1  1 
36|1.000|0.329|1.2e-10|1.5e-06|7.6e-01|-8.841501e+01 -8.862489e+01| 0:0:23| spchol  1  1 
37|1.000|0.321|9.4e-11|1.0e-06|5.2e-01|-8.841776e+01 -8.856136e+01| 0:0:23| spchol  1  1 
38|1.000|0.365|1.5e-10|3.2e-06|3.4e-01|-8.842005e+01 -8.851188e+01| 0:0:24| spchol  1  1 
39|1.000|0.930|4.5e-11|2.0e-06|3.8e-02|-8.842179e+01 -8.843101e+01| 0:0:24| spchol  1  1 
40|0.581|0.940|3.1e-11|2.3e-07|8.9e-03|-8.842275e+01 -8.842444e+01| 0:0:25| spchol  1  1 
41|0.563|0.472|1.5e-11|5.4e-08|4.7e-03|-8.842326e+01 -8.842419e+01| 0:0:26| spchol  1  1 
42|0.564|0.472|3.7e-11|2.9e-08|2.5e-03|-8.842352e+01 -8.842404e+01| 0:0:26| spchol  1  1 
43|0.566|0.472|8.1e-11|1.6e-08|1.4e-03|-8.842367e+01 -8.842395e+01| 0:0:27| spchol  1  1 
44|0.568|0.472|3.7e-11|8.3e-09|7.4e-04|-8.842374e+01 -8.842390e+01| 0:0:27| spchol  1  1 
45|0.571|0.472|1.3e-10|4.5e-09|4.1e-04|-8.842378e+01 -8.842387e+01| 0:0:28| spchol  1  1 
46|0.576|0.471|4.8e-10|2.5e-09|2.3e-04|-8.842380e+01 -8.842385e+01| 0:0:29| spchol  1  1 
47|0.586|0.471|2.2e-10|1.4e-09|1.4e-04|-8.842381e+01 -8.842384e+01| 0:0:29| spchol  1  1 
48|0.601|0.471|1.0e-10|8.4e-10|8.2e-05|-8.842382e+01 -8.842383e+01| 0:0:30| spchol  1  1 
49|0.621|0.471|3.9e-11|5.0e-10|4.8e-05|-8.842382e+01 -8.842383e+01| 0:0:30| spchol  1  1 
50|0.645|0.471|8.3e-12|2.9e-10|2.9e-05|-8.842382e+01 -8.842383e+01| 0:0:31| spchol  2  1 
51|0.675|0.471|1.5e-10|1.7e-10|1.7e-05|-8.842382e+01 -8.842383e+01| 0:0:32| spchol  2  1 
52|0.711|0.471|2.6e-11|1.0e-10|1.0e-05|-8.842382e+01 -8.842383e+01| 0:0:32| spchol  1  1 
53|0.757|0.471|1.7e-10|6.1e-11|5.9e-06|-8.842382e+01 -8.842382e+01| 0:0:33| spchol  2  1 
54|0.815|0.471|2.7e-10|3.6e-11|3.5e-06|-8.842382e+01 -8.842382e+01| 0:0:33| spchol  2  1 
55|0.893|0.471|1.9e-10|2.1e-11|2.1e-06|-8.842382e+01 -8.842382e+01| 0:0:34|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 55
 primal objective value = -8.84238241e+01
 dual   objective value = -8.84238243e+01
 gap := trace(XZ)       = 2.07e-06
 relative gap           = 1.17e-08
 actual relative gap    = 1.47e-09
 rel. primal infeas (scaled problem)   = 1.86e-10
 rel. dual     "        "       "      = 2.13e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.4e+04, 7.7e+06, 7.7e+06
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 34.06  
 CPU time per iteration = 0.62  
 termination code       =  0
 DIMACS: 1.9e-10  0.0e+00  2.0e-10  0.0e+00  1.5e-09  1.2e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +72.012
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.429126e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.055|0.229|3.9e+02|1.0e+02|1.3e+09| 1.123184e+06 -6.101479e+04| 0:0:01| spchol  1  1 
 2|0.308|0.475|2.7e+02|5.4e+01|3.2e+08| 1.918648e+06 -9.826721e+04| 0:0:01| spchol  1  1 
 3|0.855|0.818|4.0e+01|9.9e+00|4.2e+07| 2.177717e+06 -1.079942e+05| 0:0:01| spchol  1  1 
 4|0.916|0.909|3.3e+00|9.1e-01|3.7e+06| 5.817260e+05 -9.444340e+04| 0:0:02| spchol  1  1 
 5|0.697|0.604|1.0e+00|3.6e-01|1.3e+06| 2.182747e+05 -6.371932e+04| 0:0:02| spchol  1  1 
 6|0.782|0.475|2.2e-01|1.9e-01|4.3e+05| 7.064685e+04 -4.033176e+04| 0:0:02| spchol  1  1 
 7|0.432|0.299|1.2e-01|1.3e-01|2.8e+05| 4.494201e+04 -2.956698e+04| 0:0:02| spchol  1  1 
 8|0.581|0.351|5.2e-02|8.7e-02|1.5e+05| 2.396634e+04 -2.019901e+04| 0:0:03| spchol  1  1 
 9|0.664|0.387|1.8e-02|5.8e-02|8.5e+04| 1.214527e+04 -1.301106e+04| 0:0:03| spchol  1  1 
10|0.662|0.473|5.9e-03|3.3e-02|4.5e+04| 7.013205e+03 -7.252045e+03| 0:0:03| spchol  1  1 
11|0.816|0.400|1.1e-03|2.1e-02|2.2e+04| 3.361923e+03 -4.519839e+03| 0:0:03| spchol  1  1 
12|0.558|0.316|4.8e-04|1.4e-02|1.5e+04| 2.153123e+03 -3.172883e+03| 0:0:03| spchol  1  1 
13|0.381|0.186|3.0e-04|1.5e-02|1.2e+04| 1.569044e+03 -2.618296e+03| 0:0:04| spchol  1  1 
14|0.524|0.449|1.4e-04|8.5e-03|6.8e+03| 1.020168e+03 -1.504595e+03| 0:0:04| spchol  1  1 
15|0.425|0.232|8.2e-05|6.5e-03|5.1e+03| 6.917467e+02 -1.182112e+03| 0:0:04| spchol  1  1 
16|0.720|0.259|2.3e-05|4.8e-03|3.2e+03| 2.812381e+02 -8.970768e+02| 0:0:04| spchol  1  1 
17|0.493|0.257|1.2e-05|3.6e-03|2.3e+03| 1.556324e+02 -6.817857e+02| 0:0:04| spchol  1  1 
18|0.441|0.238|6.5e-06|2.7e-03|1.8e+03| 9.318640e+01 -5.325537e+02| 0:0:05| spchol  1  1 
19|0.675|0.191|2.1e-06|2.9e-03|1.3e+03| 2.123916e+01 -4.448158e+02| 0:0:05| spchol  1  1 
20|0.733|0.504|5.8e-07|1.4e-03|6.8e+02|-4.607324e+01 -2.741022e+02| 0:0:05| spchol  1  1 
21|0.951|0.353|8.9e-08|9.3e-04|4.1e+02|-1.033814e+02 -2.201052e+02| 0:0:05| spchol  1  1 
22|1.000|0.378|5.9e-08|5.8e-04|2.6e+02|-1.100729e+02 -1.815655e+02| 0:0:05| spchol  1  1 
23|1.000|0.377|3.6e-08|3.6e-04|1.6e+02|-1.126917e+02 -1.573026e+02| 0:0:06| spchol  1  1 
24|1.000|0.361|2.2e-08|2.3e-04|1.0e+02|-1.141195e+02 -1.426894e+02| 0:0:06| spchol  1  1 
25|1.000|0.335|1.5e-08|1.5e-04|7.0e+01|-1.147320e+02 -1.339170e+02| 0:0:06| spchol  1  1 
26|1.000|0.304|1.2e-08|1.1e-04|5.0e+01|-1.150205e+02 -1.286028e+02| 0:0:06| spchol  1  1 
27|0.952|0.322|8.7e-09|7.3e-05|3.5e+01|-1.153065e+02 -1.246516e+02| 0:0:06| spchol  1  1 
28|1.000|0.337|5.4e-09|4.8e-05|2.3e+01|-1.155630e+02 -1.217991e+02| 0:0:07| spchol  1  1 
29|0.959|0.401|2.9e-09|2.9e-05|1.4e+01|-1.157710e+02 -1.195173e+02| 0:0:07| spchol  1  1 
30|1.000|0.312|1.9e-09|2.0e-05|9.4e+00|-1.158491e+02 -1.184423e+02| 0:0:07| spchol  1  1 
31|1.000|0.342|1.2e-09|1.3e-05|6.2e+00|-1.159038e+02 -1.176233e+02| 0:0:07| spchol  1  1 
32|0.897|0.417|6.6e-10|7.6e-06|3.6e+00|-1.159476e+02 -1.169557e+02| 0:0:07| spchol  1  1 
33|0.908|0.354|3.6e-10|4.9e-06|2.3e+00|-1.159712e+02 -1.166212e+02| 0:0:08| spchol  1  1 
34|1.000|0.334|2.1e-10|3.3e-06|1.5e+00|-1.159822e+02 -1.164157e+02| 0:0:08| spchol  1  1 
35|1.000|0.315|1.5e-10|2.2e-06|1.1e+00|-1.159870e+02 -1.162858e+02| 0:0:08| spchol  1  1 
36|1.000|0.330|1.1e-10|1.5e-06|7.1e-01|-1.159900e+02 -1.161922e+02| 0:0:08| spchol  1  1 
37|1.000|0.325|8.0e-11|1.0e-06|4.9e-01|-1.159927e+02 -1.161302e+02| 0:0:08| spchol  1  1 
38|1.000|0.370|6.2e-11|2.9e-06|3.1e-01|-1.159948e+02 -1.160820e+02| 0:0:09| spchol  1  1 
39|0.997|0.934|3.3e-11|1.9e-06|3.3e-02|-1.159964e+02 -1.160047e+02| 0:0:09| spchol  1  1 
40|0.577|0.940|1.5e-11|2.0e-07|7.9e-03|-1.159973e+02 -1.159988e+02| 0:0:09| spchol  1  1 
41|0.562|0.472|7.4e-12|4.8e-08|4.2e-03|-1.159978e+02 -1.159986e+02| 0:0:09| spchol  1  1 
42|0.564|0.472|3.9e-11|2.5e-08|2.3e-03|-1.159980e+02 -1.159985e+02| 0:0:10| spchol  1  1 
43|0.565|0.472|6.5e-11|1.4e-08|1.2e-03|-1.159981e+02 -1.159984e+02| 0:0:10| spchol  1  1 
44|0.567|0.472|7.0e-11|7.3e-09|6.6e-04|-1.159982e+02 -1.159983e+02| 0:0:10| spchol  1  1 
45|0.570|0.472|8.2e-11|3.9e-09|3.6e-04|-1.159982e+02 -1.159983e+02| 0:0:10| spchol  1  1 
46|0.573|0.472|6.8e-11|2.2e-09|2.0e-04|-1.159982e+02 -1.159983e+02| 0:0:11| spchol  1  1 
47|0.581|0.471|1.2e-11|1.2e-09|1.2e-04|-1.159982e+02 -1.159983e+02| 0:0:11| spchol  1  1 
48|0.596|0.471|1.4e-11|7.2e-10|6.7e-05|-1.159983e+02 -1.159983e+02| 0:0:11| spchol  1  1 
49|0.608|0.471|6.6e-12|4.1e-10|4.0e-05|-1.159983e+02 -1.159983e+02| 0:0:11| spchol  1  1 
50|0.629|0.471|1.8e-12|2.4e-10|2.3e-05|-1.159983e+02 -1.159983e+02| 0:0:12| spchol  2  1 
51|0.650|0.471|1.6e-11|1.4e-10|1.4e-05|-1.159983e+02 -1.159983e+02| 0:0:12| spchol  2  1 
52|0.681|0.471|1.2e-11|8.3e-11|8.1e-06|-1.159983e+02 -1.159983e+02| 0:0:12| spchol  1  1 
53|0.719|0.471|5.3e-12|4.9e-11|4.8e-06|-1.159983e+02 -1.159983e+02| 0:0:13| spchol  2  1 
54|0.767|0.471|5.2e-11|2.9e-11|2.8e-06|-1.159983e+02 -1.159983e+02| 0:0:13|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 54
 primal objective value = -1.15998259e+02
 dual   objective value = -1.15998259e+02
 gap := trace(XZ)       = 2.84e-06
 relative gap           = 1.22e-08
 actual relative gap    = 1.68e-09
 rel. primal infeas (scaled problem)   = 5.22e-11
 rel. dual     "        "       "      = 2.90e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.3e+04, 7.6e+06, 7.6e+06
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 12.94  
 CPU time per iteration = 0.24  
 termination code       =  0
 DIMACS: 5.3e-11  0.0e+00  2.2e-10  0.0e+00  1.7e-09  1.2e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +101.836
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.435126e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.056|0.232|3.9e+02|1.0e+02|1.3e+09| 1.126720e+06 -6.114468e+04| 0:0:01| spchol  1  1 
 2|0.319|0.480|2.7e+02|5.3e+01|3.2e+08| 1.948488e+06 -9.875094e+04| 0:0:02| spchol  1  1 
 3|0.859|0.819|3.8e+01|9.6e+00|4.1e+07| 2.181385e+06 -1.083072e+05| 0:0:02| spchol  1  1 
 4|0.923|0.909|2.9e+00|8.9e-01|3.4e+06| 5.637820e+05 -9.416936e+04| 0:0:03| spchol  1  1 
 5|0.709|0.618|8.5e-01|3.4e-01|1.2e+06| 2.038107e+05 -6.074195e+04| 0:0:04| spchol  1  1 
 6|0.777|0.470|1.9e-01|1.8e-01|3.9e+05| 6.628797e+04 -3.807374e+04| 0:0:04| spchol  1  1 
 7|0.418|0.285|1.1e-01|1.3e-01|2.6e+05| 4.303490e+04 -2.837242e+04| 0:0:05| spchol  1  1 
 8|0.615|0.356|4.2e-02|8.4e-02|1.4e+05| 2.193807e+04 -1.920337e+04| 0:0:06| spchol  1  1 
 9|0.625|0.470|1.6e-02|4.9e-02|7.5e+04| 1.191341e+04 -1.085602e+04| 0:0:06| spchol  1  1 
10|0.589|0.399|6.6e-03|3.2e-02|4.4e+04| 7.277164e+03 -6.821842e+03| 0:0:07| spchol  1  1 
11|0.785|0.381|1.4e-03|2.1e-02|2.2e+04| 3.471020e+03 -4.382263e+03| 0:0:07| spchol  1  1 
12|0.576|0.304|6.0e-04|1.5e-02|1.5e+04| 2.132284e+03 -3.126799e+03| 0:0:08| spchol  1  1 
13|0.426|0.211|3.4e-04|1.2e-02|1.1e+04| 1.474231e+03 -2.506341e+03| 0:0:09| spchol  1  1 
14|0.476|0.328|1.8e-04|7.9e-03|7.5e+03| 9.757284e+02 -1.734853e+03| 0:0:09| spchol  1  1 
15|0.792|0.199|3.7e-05|8.1e-03|5.1e+03| 3.889632e+02 -1.412303e+03| 0:0:10| spchol  1  1 
16|0.852|0.557|5.6e-06|3.6e-03|2.2e+03| 1.371929e+02 -6.648593e+02| 0:0:10| spchol  1  1 
17|0.421|0.275|3.2e-06|2.6e-03|1.6e+03| 7.433201e+01 -5.004102e+02| 0:0:11| spchol  1  1 
18|0.645|0.196|1.2e-06|2.7e-03|1.2e+03|-1.907714e+01 -4.276118e+02| 0:0:12| spchol  1  1 
19|0.908|0.504|1.4e-07|1.3e-03|5.9e+02|-1.139577e+02 -2.900275e+02| 0:0:12| spchol  1  1 
20|0.953|0.440|6.9e-08|7.5e-04|3.3e+02|-1.347198e+02 -2.266837e+02| 0:0:13| spchol  1  1 
21|1.000|0.363|4.2e-08|4.8e-04|2.1e+02|-1.390286e+02 -1.970687e+02| 0:0:13| spchol  1  1 
22|1.000|0.358|2.6e-08|3.1e-04|1.4e+02|-1.410271e+02 -1.782479e+02| 0:0:14| spchol  1  1 
23|1.000|0.340|1.9e-08|2.0e-04|9.2e+01|-1.418616e+02 -1.667010e+02| 0:0:15| spchol  1  1 
24|1.000|0.342|1.2e-08|1.3e-04|6.1e+01|-1.424876e+02 -1.589465e+02| 0:0:15| spchol  1  1 
25|1.000|0.296|9.4e-09|9.4e-05|4.4e+01|-1.427384e+02 -1.545061e+02| 0:0:16| spchol  1  1 
26|0.951|0.327|6.9e-09|6.3e-05|3.0e+01|-1.429844e+02 -1.510326e+02| 0:0:16| spchol  1  1 
27|1.000|0.353|3.9e-09|4.1e-05|1.9e+01|-1.432467e+02 -1.484625e+02| 0:0:17| spchol  1  1 
28|0.958|0.405|2.1e-09|2.4e-05|1.1e+01|-1.434094e+02 -1.465232e+02| 0:0:18| spchol  1  1 
29|1.000|0.283|1.6e-09|1.7e-05|8.3e+00|-1.434558e+02 -1.457125e+02| 0:0:18| spchol  1  1 
30|1.000|0.354|1.0e-09|1.1e-05|5.4e+00|-1.435046e+02 -1.449774e+02| 0:0:19| spchol  1  1 
31|0.912|0.401|5.3e-10|6.8e-06|3.2e+00|-1.435434e+02 -1.444288e+02| 0:0:19| spchol  1  1 
32|0.874|0.388|2.8e-10|4.1e-06|1.9e+00|-1.435647e+02 -1.441070e+02| 0:0:20| spchol  1  1 
33|1.000|0.314|1.6e-10|2.8e-06|1.3e+00|-1.435756e+02 -1.439465e+02| 0:0:21| spchol  1  1 
34|1.000|0.328|1.2e-10|1.9e-06|9.0e-01|-1.435788e+02 -1.438310e+02| 0:0:21| spchol  1  1 
35|1.000|0.310|9.6e-11|1.3e-06|6.2e-01|-1.435816e+02 -1.437571e+02| 0:0:22| spchol  1  1 
36|1.000|0.350|6.5e-11|3.7e-06|4.1e-01|-1.435839e+02 -1.436992e+02| 0:0:22| spchol  1  1 
37|1.000|0.927|4.1e-11|2.5e-06|5.4e-02|-1.435854e+02 -1.435985e+02| 0:0:23| spchol  1  1 
38|0.607|0.928|2.1e-11|3.2e-07|1.5e-02|-1.435871e+02 -1.435899e+02| 0:0:24| spchol  1  1 
39|0.562|0.472|1.2e-11|8.7e-08|7.8e-03|-1.435879e+02 -1.435895e+02| 0:0:24| spchol  1  1 
40|0.563|0.472|1.6e-11|4.7e-08|4.2e-03|-1.435883e+02 -1.435892e+02| 0:0:25| spchol  1  1 
41|0.565|0.472|4.1e-11|2.5e-08|2.3e-03|-1.435886e+02 -1.435890e+02| 0:0:25| spchol  1  1 
42|0.567|0.472|4.3e-11|1.3e-08|1.2e-03|-1.435887e+02 -1.435890e+02| 0:0:26| spchol  1  1 
43|0.569|0.472|5.3e-11|7.2e-09|6.6e-04|-1.435888e+02 -1.435889e+02| 0:0:27| spchol  1  1 
44|0.572|0.472|8.0e-13|3.9e-09|3.7e-04|-1.435888e+02 -1.435889e+02| 0:0:27| spchol  1  1 
45|0.579|0.471|1.0e-11|2.2e-09|2.0e-04|-1.435888e+02 -1.435889e+02| 0:0:28| spchol  1  1 
46|0.581|0.471|6.1e-11|1.2e-09|1.1e-04|-1.435888e+02 -1.435888e+02| 0:0:28| spchol  1  1 
47|0.585|0.471|6.2e-11|6.5e-10|6.1e-05|-1.435888e+02 -1.435888e+02| 0:0:29| spchol  1  1 
48|0.594|0.471|4.7e-12|3.7e-10|3.6e-05|-1.435888e+02 -1.435888e+02| 0:0:30| spchol  1  1 
49|0.613|0.471|6.9e-12|2.2e-10|2.1e-05|-1.435888e+02 -1.435888e+02| 0:0:30| spchol  2  1 
50|0.629|0.471|4.8e-11|1.2e-10|1.2e-05|-1.435888e+02 -1.435888e+02| 0:0:31| spchol  1  1 
51|0.655|0.471|1.8e-11|7.4e-11|7.3e-06|-1.435888e+02 -1.435888e+02| 0:0:32| spchol  2  1 
52|0.687|0.471|1.2e-11|4.4e-11|4.3e-06|-1.435888e+02 -1.435888e+02| 0:0:32| spchol  2  1 
53|0.727|0.471|3.8e-11|2.6e-11|2.6e-06|-1.435888e+02 -1.435888e+02| 0:0:33|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 53
 primal objective value = -1.43588830e+02
 dual   objective value = -1.43588831e+02
 gap := trace(XZ)       = 2.55e-06
 relative gap           = 8.85e-09
 actual relative gap    = 1.36e-09
 rel. primal infeas (scaled problem)   = 3.80e-11
 rel. dual     "        "       "      = 2.57e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.4e+04, 8.5e+06, 8.5e+06
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 32.82  
 CPU time per iteration = 0.62  
 termination code       =  0
 DIMACS: 3.8e-11  0.0e+00  1.7e-10  0.0e+00  1.4e-09  8.9e-09
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +132.177
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.441126e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.057|0.235|3.9e+02|1.0e+02|1.2e+09| 1.130773e+06 -6.132182e+04| 0:0:01| spchol  1  1 
 2|0.333|0.486|2.6e+02|5.1e+01|3.1e+08| 1.985809e+06 -9.932775e+04| 0:0:01| spchol  1  1 
 3|0.865|0.821|3.5e+01|9.2e+00|3.9e+07| 2.176559e+06 -1.084960e+05| 0:0:01| spchol  1  1 
 4|0.927|0.908|2.6e+00|8.6e-01|3.1e+06| 5.422950e+05 -9.353832e+04| 0:0:02| spchol  1  1 
 5|0.723|0.641|7.1e-01|3.1e-01|1.0e+06| 1.875748e+05 -5.721099e+04| 0:0:02| spchol  1  1 
 6|0.740|0.440|1.9e-01|1.8e-01|3.8e+05| 6.647898e+04 -3.677196e+04| 0:0:02| spchol  1  1 
 7|0.441|0.292|1.0e-01|1.2e-01|2.5e+05| 4.197190e+04 -2.721265e+04| 0:0:02| spchol  1  1 
 8|0.676|0.393|3.4e-02|7.6e-02|1.2e+05| 1.935119e+04 -1.743783e+04| 0:0:02| spchol  1  1 
 9|0.544|0.498|1.5e-02|4.2e-02|6.8e+04| 1.181563e+04 -9.387188e+03| 0:0:03| spchol  1  1 
10|0.543|0.396|7.0e-03|2.8e-02|4.2e+04| 7.402646e+03 -5.937873e+03| 0:0:03| spchol  1  1 
11|0.707|0.327|2.0e-03|2.0e-02|2.3e+04| 3.704937e+03 -4.124084e+03| 0:0:03| spchol  1  1 
12|0.565|0.294|8.9e-04|1.4e-02|1.5e+04| 2.226519e+03 -2.988852e+03| 0:0:03| spchol  1  1 
13|0.456|0.216|4.8e-04|1.1e-02|1.1e+04| 1.462660e+03 -2.384478e+03| 0:0:03| spchol  1  1 
14|0.547|0.287|2.2e-04|8.1e-03|7.5e+03| 8.817101e+02 -1.742978e+03| 0:0:04| spchol  1  1 
15|0.836|0.249|3.6e-05|6.1e-03|4.8e+03| 3.195646e+02 -1.335955e+03| 0:0:04| spchol  1  1 
16|0.755|0.331|8.8e-06|4.1e-03|3.1e+03| 1.317177e+02 -9.205243e+02| 0:0:04| spchol  1  1 
17|0.598|0.307|3.6e-06|2.9e-03|2.2e+03| 5.719181e+01 -6.641193e+02| 0:0:04| spchol  1  1 
18|0.829|0.246|6.3e-07|2.2e-03|1.6e+03|-5.264891e+01 -5.360079e+02| 0:0:04| spchol  1  1 
19|0.643|0.395|2.4e-07|1.3e-03|9.6e+02|-1.117056e+02 -3.945856e+02| 0:0:05| spchol  1  1 
20|0.934|0.302|8.0e-08|9.1e-04|6.5e+02|-1.543359e+02 -3.288584e+02| 0:0:05| spchol  1  1 
21|1.000|0.332|6.2e-08|6.1e-04|4.5e+02|-1.619670e+02 -2.776564e+02| 0:0:05| spchol  1  1 
22|1.000|0.358|4.0e-08|3.9e-04|2.9e+02|-1.657876e+02 -2.403133e+02| 0:0:05| spchol  1  1 
23|1.000|0.368|2.5e-08|2.5e-04|1.8e+02|-1.680380e+02 -2.153945e+02| 0:0:06| spchol  1  1 
24|1.000|0.305|1.9e-08|1.7e-04|1.3e+02|-1.689116e+02 -2.022424e+02| 0:0:06| spchol  1  1 
25|1.000|0.325|1.4e-08|1.2e-04|9.0e+01|-1.695584e+02 -1.924270e+02| 0:0:06| spchol  1  1 
26|1.000|0.346|8.8e-09|7.6e-05|5.9e+01|-1.701749e+02 -1.852512e+02| 0:0:06| spchol  1  1 
27|1.000|0.310|6.5e-09|5.2e-05|4.1e+01|-1.704677e+02 -1.810232e+02| 0:0:07| spchol  1  1 
28|1.000|0.349|4.1e-09|3.4e-05|2.7e+01|-1.707597e+02 -1.776896e+02| 0:0:07| spchol  1  1 
29|1.000|0.381|2.2e-09|2.1e-05|1.7e+01|-1.709804e+02 -1.752801e+02| 0:0:07| spchol  1  1 
30|1.000|0.369|1.2e-09|1.3e-05|1.0e+01|-1.710882e+02 -1.738135e+02| 0:0:07| spchol  1  1 
31|1.000|0.283|1.0e-09|9.5e-06|7.6e+00|-1.711145e+02 -1.731006e+02| 0:0:08| spchol  1  1 
32|1.000|0.329|7.4e-10|6.4e-06|5.2e+00|-1.711482e+02 -1.725010e+02| 0:0:08| spchol  1  1 
33|0.903|0.407|3.9e-10|3.8e-06|3.1e+00|-1.711860e+02 -1.719928e+02| 0:0:08| spchol  1  1 
34|0.880|0.375|2.1e-10|2.4e-06|1.9e+00|-1.712065e+02 -1.717106e+02| 0:0:08| spchol  1  1 
35|1.000|0.291|1.5e-10|1.7e-06|1.3e+00|-1.712151e+02 -1.715729e+02| 0:0:09| spchol  1  1 
36|1.000|0.317|1.0e-10|1.1e-06|9.3e-01|-1.712186e+02 -1.714662e+02| 0:0:09| spchol  1  1 
37|1.000|0.319|9.3e-11|7.8e-07|6.4e-01|-1.712219e+02 -1.713923e+02| 0:0:09| spchol  1  1 
38|1.000|0.345|8.8e-11|3.7e-06|4.3e-01|-1.712246e+02 -1.713372e+02| 0:0:09| spchol  1  1 
39|1.000|0.891|3.0e-11|2.5e-06|6.7e-02|-1.712268e+02 -1.712431e+02| 0:0:10| spchol  1  1 
40|0.581|0.929|1.7e-11|3.9e-07|1.5e-02|-1.712282e+02 -1.712311e+02| 0:0:10| spchol  1  1 
41|0.571|0.472|8.3e-12|8.6e-08|7.8e-03|-1.712290e+02 -1.712306e+02| 0:0:10| spchol  1  1 
42|0.573|0.472|4.1e-12|4.6e-08|4.2e-03|-1.712294e+02 -1.712303e+02| 0:0:10| spchol  1  1 
43|0.575|0.472|9.2e-12|2.5e-08|2.2e-03|-1.712296e+02 -1.712301e+02| 0:0:10| spchol  1  1 
44|0.576|0.472|9.7e-12|1.3e-08|1.2e-03|-1.712297e+02 -1.712300e+02| 0:0:11| spchol  1  1 
45|0.578|0.472|3.4e-12|7.1e-09|6.5e-04|-1.712298e+02 -1.712299e+02| 0:0:11| spchol  1  1 
46|0.581|0.472|6.3e-12|3.8e-09|3.5e-04|-1.712298e+02 -1.712299e+02| 0:0:11| spchol  1  1 
47|0.583|0.471|9.3e-12|2.1e-09|1.9e-04|-1.712298e+02 -1.712299e+02| 0:0:11| spchol  1  1 
48|0.586|0.471|9.8e-12|1.1e-09|1.0e-04|-1.712298e+02 -1.712299e+02| 0:0:12| spchol  1  1 
49|0.591|0.471|9.9e-12|6.1e-10|5.8e-05|-1.712298e+02 -1.712299e+02| 0:0:12| spchol  1  1 
50|0.599|0.471|2.7e-12|3.4e-10|3.4e-05|-1.712299e+02 -1.712299e+02| 0:0:12| spchol  1  1 
51|0.614|0.471|1.7e-11|2.0e-10|1.9e-05|-1.712299e+02 -1.712299e+02| 0:0:12| spchol  1  1 
52|0.631|0.471|3.6e-12|1.1e-10|1.1e-05|-1.712299e+02 -1.712299e+02| 0:0:13| spchol  1  1 
53|0.658|0.471|5.2e-12|6.8e-11|6.8e-06|-1.712299e+02 -1.712299e+02| 0:0:13| spchol  2  1 
54|0.690|0.471|3.6e-12|4.0e-11|4.0e-06|-1.712299e+02 -1.712299e+02| 0:0:13|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 54
 primal objective value = -1.71229854e+02
 dual   objective value = -1.71229855e+02
 gap := trace(XZ)       = 4.01e-06
 relative gap           = 1.17e-08
 actual relative gap    = 2.01e-09
 rel. primal infeas (scaled problem)   = 3.60e-12
 rel. dual     "        "       "      = 4.01e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.0e+04, 1.1e+07, 1.1e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.0e+02
 Total CPU time (secs)  = 13.06  
 CPU time per iteration = 0.24  
 termination code       =  0
 DIMACS: 3.6e-12  0.0e+00  2.2e-10  0.0e+00  2.0e-09  1.2e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +163.068
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.8e+09| 7.447126e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.059|0.239|3.9e+02|9.8e+01|1.2e+09| 1.135294e+06 -6.155294e+04| 0:0:01| spchol  1  1 
 2|0.349|0.493|2.6e+02|5.0e+01|3.1e+08| 2.031241e+06 -9.998773e+04| 0:0:01| spchol  1  1 
 3|0.873|0.824|3.3e+01|8.8e+00|3.7e+07| 2.167619e+06 -1.086495e+05| 0:0:01| spchol  1  1 
 4|0.919|0.907|2.6e+00|8.3e-01|3.2e+06| 5.378348e+05 -9.259465e+04| 0:0:02| spchol  1  1 
 5|0.729|0.654|7.2e-01|2.9e-01|1.0e+06| 1.835417e+05 -5.616103e+04| 0:0:02| spchol  1  1 
 6|0.704|0.405|2.1e-01|1.7e-01|4.1e+05| 7.086677e+04 -3.786077e+04| 0:0:02| spchol  1  1 
 7|0.473|0.312|1.1e-01|1.2e-01|2.6e+05| 4.298185e+04 -2.741567e+04| 0:0:03| spchol  1  1 
 8|0.701|0.439|3.4e-02|6.7e-02|1.1e+05| 1.899522e+04 -1.642081e+04| 0:0:03| spchol  1  1 
 9|0.514|0.493|1.6e-02|3.8e-02|6.7e+04| 1.194618e+04 -8.902312e+03| 0:0:03| spchol  1  1 
10|0.535|0.348|7.6e-03|2.7e-02|4.2e+04| 7.428143e+03 -6.022967e+03| 0:0:03| spchol  1  1 
11|0.746|0.294|1.9e-03|2.0e-02|2.3e+04| 3.475891e+03 -4.366538e+03| 0:0:04| spchol  1  1 
12|0.644|0.332|6.8e-04|1.4e-02|1.4e+04| 1.929123e+03 -3.001723e+03| 0:0:04| spchol  1  1 
13|0.482|0.247|3.5e-04|1.1e-02|1.0e+04| 1.236924e+03 -2.302415e+03| 0:0:04| spchol  1  1 
14|0.569|0.297|1.5e-04|7.5e-03|6.9e+03| 7.262901e+02 -1.661526e+03| 0:0:04| spchol  1  1 
15|0.873|0.267|2.0e-05|5.5e-03|4.3e+03| 2.291511e+02 -1.245503e+03| 0:0:05| spchol  1  1 
16|0.669|0.338|6.5e-06|3.7e-03|2.9e+03| 9.913732e+01 -8.548926e+02| 0:0:05| spchol  1  1 
17|0.750|0.270|1.6e-06|2.7e-03|2.0e+03|-8.730606e+00 -6.608316e+02| 0:0:05| spchol  1  1 
18|0.910|0.305|2.1e-07|1.9e-03|1.4e+03|-1.352896e+02 -5.231140e+02| 0:0:05| spchol  1  1 
19|0.646|0.439|1.1e-07|1.0e-03|7.9e+02|-1.647572e+02 -3.840385e+02| 0:0:06| spchol  1  1 
20|1.000|0.271|7.0e-08|7.6e-04|5.7e+02|-1.873214e+02 -3.351089e+02| 0:0:06| spchol  1  1 
21|1.000|0.356|5.2e-08|4.9e-04|3.8e+02|-1.913692e+02 -2.877566e+02| 0:0:06| spchol  1  1 
22|1.000|0.369|3.1e-08|3.1e-04|2.4e+02|-1.947550e+02 -2.556289e+02| 0:0:06| spchol  1  1 
23|1.000|0.350|2.1e-08|2.0e-04|1.6e+02|-1.963585e+02 -2.362294e+02| 0:0:07| spchol  1  1 
24|1.000|0.298|1.6e-08|1.4e-04|1.1e+02|-1.970274e+02 -2.254174e+02| 0:0:07| spchol  1  1 
25|1.000|0.313|1.3e-08|9.7e-05|7.9e+01|-1.975324e+02 -2.173839e+02| 0:0:07| spchol  1  1 
26|1.000|0.322|8.9e-09|6.6e-05|5.4e+01|-1.980140e+02 -2.116512e+02| 0:0:07| spchol  1  1 
27|1.000|0.340|5.9e-09|4.3e-05|3.6e+01|-1.983940e+02 -2.075024e+02| 0:0:08| spchol  1  1 
28|1.000|0.373|3.2e-09|2.7e-05|2.2e+01|-1.987087e+02 -2.044403e+02| 0:0:08| spchol  1  1 
29|0.876|0.419|1.7e-09|1.6e-05|1.3e+01|-1.988873e+02 -2.022358e+02| 0:0:08| spchol  1  1 
30|0.883|0.351|9.1e-10|1.0e-05|8.3e+00|-1.989815e+02 -2.011478e+02| 0:0:08| spchol  1  1 
31|1.000|0.344|4.8e-10|6.7e-06|5.4e+00|-1.990319e+02 -2.004502e+02| 0:0:09| spchol  1  1 
32|1.000|0.367|2.7e-10|4.3e-06|3.4e+00|-1.990567e+02 -1.999558e+02| 0:0:10| spchol  1  1 
33|1.000|0.360|1.7e-10|2.7e-06|2.2e+00|-1.990687e+02 -1.996469e+02| 0:0:10| spchol  1  1 
34|1.000|0.298|1.3e-10|1.9e-06|1.5e+00|-1.990733e+02 -1.994826e+02| 0:0:11| spchol  1  1 
35|1.000|0.309|1.0e-10|1.3e-06|1.1e+00|-1.990762e+02 -1.993627e+02| 0:0:11| spchol  1  1 
36|1.000|0.305|7.8e-11|9.2e-07|7.6e-01|-1.990790e+02 -1.992803e+02| 0:0:12| spchol  1  1 
37|1.000|0.328|5.6e-11|6.2e-07|5.2e-01|-1.990815e+02 -1.992183e+02| 0:0:13| spchol  1  1 
38|1.000|0.332|4.6e-11|2.9e-06|3.5e-01|-1.990837e+02 -1.991757e+02| 0:0:13| spchol  1  1 
39|1.000|0.889|2.3e-11|2.0e-06|5.6e-02|-1.990853e+02 -1.990989e+02| 0:0:14| spchol  1  1 
40|0.578|0.929|1.3e-11|3.3e-07|1.2e-02|-1.990866e+02 -1.990889e+02| 0:0:15| spchol  1  1 
41|0.571|0.472|6.4e-12|7.1e-08|6.5e-03|-1.990872e+02 -1.990885e+02| 0:0:15| spchol  1  1 
42|0.573|0.472|5.3e-12|3.8e-08|3.5e-03|-1.990875e+02 -1.990883e+02| 0:0:16| spchol  1  1 
43|0.575|0.472|2.0e-11|2.0e-08|1.9e-03|-1.990877e+02 -1.990881e+02| 0:0:17| spchol  1  1 
44|0.576|0.472|1.4e-12|1.1e-08|1.0e-03|-1.990878e+02 -1.990880e+02| 0:0:17| spchol  1  1 
45|0.579|0.471|6.8e-12|5.9e-09|5.4e-04|-1.990879e+02 -1.990880e+02| 0:0:18| spchol  1  1 
46|0.581|0.471|2.2e-11|3.2e-09|2.9e-04|-1.990879e+02 -1.990880e+02| 0:0:18| spchol  1  1 
47|0.583|0.471|1.1e-11|1.7e-09|1.6e-04|-1.990879e+02 -1.990879e+02| 0:0:19| spchol  1  1 
48|0.587|0.471|1.9e-11|9.3e-10|8.8e-05|-1.990879e+02 -1.990879e+02| 0:0:20| spchol  1  1 
49|0.594|0.471|1.1e-12|5.2e-10|5.1e-05|-1.990879e+02 -1.990879e+02| 0:0:20| spchol  1  1 
50|0.609|0.471|1.0e-11|3.0e-10|2.9e-05|-1.990879e+02 -1.990879e+02| 0:0:21| spchol  1  1 
51|0.621|0.471|1.3e-11|1.7e-10|1.7e-05|-1.990879e+02 -1.990879e+02| 0:0:22| spchol  1  1 
52|0.643|0.471|6.1e-12|1.0e-10|1.0e-05|-1.990879e+02 -1.990879e+02| 0:0:22| spchol  1  1 
53|0.672|0.471|7.9e-12|5.9e-11|6.0e-06|-1.990879e+02 -1.990879e+02| 0:0:23| spchol  1  1 
54|0.708|0.471|5.8e-12|3.5e-11|3.5e-06|-1.990879e+02 -1.990879e+02| 0:0:24|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 54
 primal objective value = -1.99087912e+02
 dual   objective value = -1.99087913e+02
 gap := trace(XZ)       = 3.53e-06
 relative gap           = 8.85e-09
 actual relative gap    = 1.47e-09
 rel. primal infeas (scaled problem)   = 5.80e-12
 rel. dual     "        "       "      = 3.48e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 2.9e+04, 1.2e+07, 1.2e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.1e+02
 Total CPU time (secs)  = 23.71  
 CPU time per iteration = 0.44  
 termination code       =  0
 DIMACS: 5.9e-12  0.0e+00  1.7e-10  0.0e+00  1.5e-09  8.8e-09
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +194.676
 

 
Calling SDPT3 4.0: 8512 variables, 3388 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 3388
 dim. of sdp    var  = 170,   num. of sdp  blk  = 57
 dim. of socp   var  = 6272,   num. of socp blk  = 1596
 dim. of linear var  = 223
 dim. of free   var  = 138 *** convert ublk to lblk
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|4.2e+02|1.3e+02|6.9e+09| 7.453126e+05  0.000000e+00| 0:0:00| spchol  1  1 
 1|0.061|0.244|3.9e+02|9.7e+01|1.2e+09| 1.140234e+06 -6.184180e+04| 0:0:00| spchol  1  1 
 2|0.369|0.500|2.5e+02|4.8e+01|3.0e+08| 2.085630e+06 -1.007195e+05| 0:0:01| spchol  1  1 
 3|0.882|0.830|2.9e+01|8.2e+00|3.4e+07| 2.153403e+06 -1.087302e+05| 0:0:01| spchol  1  1 
 4|0.907|0.905|2.7e+00|7.9e-01|3.2e+06| 5.321630e+05 -9.119028e+04| 0:0:01| spchol  1  1 
 5|0.709|0.658|7.9e-01|2.7e-01|1.1e+06| 1.907960e+05 -5.530791e+04| 0:0:01| spchol  1  1 
 6|0.671|0.376|2.6e-01|1.7e-01|4.6e+05| 7.861781e+04 -3.894170e+04| 0:0:02| spchol  1  1 
 7|0.483|0.320|1.3e-01|1.2e-01|2.8e+05| 4.697489e+04 -2.804189e+04| 0:0:02| spchol  1  1 
 8|0.716|0.431|3.8e-02|6.7e-02|1.2e+05| 2.002358e+04 -1.706743e+04| 0:0:02| spchol  1  1 
 9|0.554|0.507|1.7e-02|3.7e-02|6.7e+04| 1.204135e+04 -9.030339e+03| 0:0:02| spchol  1  1 
10|0.539|0.373|7.8e-03|2.6e-02|4.2e+04| 7.443594e+03 -5.899492e+03| 0:0:02| spchol  1  1 
11|0.765|0.308|1.8e-03|1.9e-02|2.2e+04| 3.317603e+03 -4.195459e+03| 0:0:03| spchol  1  1 
12|0.658|0.320|6.3e-04|1.3e-02|1.4e+04| 1.775714e+03 -2.930466e+03| 0:0:03| spchol  1  1 
13|0.485|0.271|3.2e-04|9.7e-03|9.6e+03| 1.125295e+03 -2.181595e+03| 0:0:03| spchol  1  1 
14|0.551|0.265|1.5e-04|7.2e-03|6.8e+03| 6.659012e+02 -1.640826e+03| 0:0:03| spchol  1  1 
15|0.877|0.257|1.8e-05|5.4e-03|4.3e+03| 2.020822e+02 -1.247135e+03| 0:0:03| spchol  1  1 
16|0.735|0.351|4.8e-06|3.5e-03|2.8e+03| 6.179225e+01 -8.482712e+02| 0:0:04| spchol  1  1 
17|0.754|0.284|1.2e-06|2.5e-03|2.0e+03|-6.799229e+01 -6.642807e+02| 0:0:04| spchol  1  1 
18|0.672|0.337|4.3e-07|1.7e-03|1.3e+03|-1.501971e+02 -5.219207e+02| 0:0:04| spchol  1  1 
19|0.680|0.329|1.6e-07|1.1e-03|8.7e+02|-1.892827e+02 -4.274457e+02| 0:0:04| spchol  1  1 
20|1.000|0.256|8.1e-08|8.3e-04|6.5e+02|-2.129795e+02 -3.774770e+02| 0:0:05| spchol  1  1 
21|1.000|0.369|5.8e-08|5.2e-04|4.2e+02|-2.182687e+02 -3.231533e+02| 0:0:05| spchol  1  1 
22|1.000|0.340|4.1e-08|3.4e-04|2.8e+02|-2.216156e+02 -2.912468e+02| 0:0:05| spchol  1  1 
23|1.000|0.353|2.7e-08|2.2e-04|1.8e+02|-2.237448e+02 -2.691058e+02| 0:0:05| spchol  1  1 
24|1.000|0.410|1.3e-08|1.3e-04|1.1e+02|-2.255415e+02 -2.521674e+02| 0:0:05| spchol  1  1 
25|1.000|0.350|8.0e-09|8.6e-05|6.9e+01|-2.261660e+02 -2.435584e+02| 0:0:06| spchol  1  1 
26|1.000|0.292|6.3e-09|6.1e-05|5.0e+01|-2.263767e+02 -2.388553e+02| 0:0:06| spchol  1  1 
27|1.000|0.304|5.1e-09|4.2e-05|3.5e+01|-2.265174e+02 -2.353771e+02| 0:0:06| spchol  1  1 
28|1.000|0.309|3.8e-09|2.9e-05|2.5e+01|-2.266682e+02 -2.328926e+02| 0:0:06| spchol  1  1 
29|1.000|0.345|2.5e-09|1.9e-05|1.6e+01|-2.268195e+02 -2.309464e+02| 0:0:06| spchol  1  1 
30|1.000|0.376|1.4e-09|1.2e-05|1.0e+01|-2.269493e+02 -2.295344e+02| 0:0:07| spchol  1  1 
31|0.881|0.418|7.3e-10|6.9e-06|5.9e+00|-2.270212e+02 -2.285351e+02| 0:0:07| spchol  1  1 
32|0.855|0.361|3.8e-10|4.4e-06|3.7e+00|-2.270594e+02 -2.280244e+02| 0:0:07| spchol  1  1 
33|0.922|0.348|2.0e-10|2.9e-06|2.4e+00|-2.270798e+02 -2.277078e+02| 0:0:07| spchol  1  1 
34|1.000|0.333|1.2e-10|1.9e-06|1.6e+00|-2.270898e+02 -2.275084e+02| 0:0:07| spchol  1  1 
35|1.000|0.355|7.4e-11|1.2e-06|1.0e+00|-2.270944e+02 -2.273660e+02| 0:0:08| spchol  1  1 
36|1.000|0.306|5.5e-11|8.6e-07|7.2e-01|-2.270965e+02 -2.272865e+02| 0:0:08| spchol  1  1 
37|1.000|0.303|4.8e-11|6.0e-07|5.1e-01|-2.270978e+02 -2.272315e+02| 0:0:08| spchol  1  1 
38|1.000|0.318|4.0e-11|2.8e-06|3.6e-01|-2.270990e+02 -2.271911e+02| 0:0:08| spchol  1  1 
39|1.000|0.893|2.2e-11|2.0e-06|5.5e-02|-2.271002e+02 -2.271132e+02| 0:0:08| spchol  1  1 
40|0.602|0.930|1.2e-11|3.1e-07|1.2e-02|-2.271013e+02 -2.271036e+02| 0:0:09| spchol  1  1 
41|0.573|0.472|6.4e-12|6.7e-08|6.2e-03|-2.271019e+02 -2.271032e+02| 0:0:09| spchol  1  1 
42|0.574|0.471|3.5e-12|3.5e-08|3.3e-03|-2.271022e+02 -2.271029e+02| 0:0:09| spchol  1  1 
43|0.576|0.471|2.2e-12|1.9e-08|1.8e-03|-2.271024e+02 -2.271028e+02| 0:0:09| spchol  1  1 
44|0.578|0.471|4.9e-12|1.0e-08|9.6e-04|-2.271025e+02 -2.271027e+02| 0:0:09| spchol  1  1 
45|0.580|0.471|6.8e-13|5.5e-09|5.2e-04|-2.271025e+02 -2.271026e+02| 0:0:10| spchol  1  1 
46|0.582|0.471|2.1e-11|3.0e-09|2.8e-04|-2.271025e+02 -2.271026e+02| 0:0:10| spchol  1  1 
47|0.585|0.471|3.5e-12|1.6e-09|1.5e-04|-2.271026e+02 -2.271026e+02| 0:0:10| spchol  1  1 
48|0.588|0.471|4.3e-12|8.7e-10|8.2e-05|-2.271026e+02 -2.271026e+02| 0:0:10| spchol  1  1 
49|0.591|0.471|5.6e-11|4.8e-10|4.6e-05|-2.271026e+02 -2.271026e+02| 0:0:10| spchol  1  1 
50|0.598|0.471|6.2e-11|2.6e-10|2.6e-05|-2.271026e+02 -2.271026e+02| 0:0:10| spchol  1  1 
51|0.614|0.471|7.0e-12|1.5e-10|1.6e-05|-2.271026e+02 -2.271026e+02| 0:0:11| spchol  1  1 
52|0.637|0.471|2.4e-11|9.1e-11|9.2e-06|-2.271026e+02 -2.271026e+02| 0:0:11| spchol  1  1 
53|0.665|0.471|4.1e-11|5.4e-11|5.5e-06|-2.271026e+02 -2.271026e+02| 0:0:11|
  stop: max(relative gap, infeasibilities) < 1.49e-08
-------------------------------------------------------------------
 number of iterations   = 53
 primal objective value = -2.27102575e+02
 dual   objective value = -2.27102576e+02
 gap := trace(XZ)       = 5.46e-06
 relative gap           = 1.20e-08
 actual relative gap    = 2.21e-09
 rel. primal infeas (scaled problem)   = 4.09e-11
 rel. dual     "        "       "      = 5.35e-11
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 2.9e+04, 1.1e+07, 1.1e+07
 norm(A), norm(b), norm(C) = 1.2e+02, 5.8e+01, 2.1e+02
 Total CPU time (secs)  = 11.08  
 CPU time per iteration = 0.21  
 termination code       =  0
 DIMACS: 4.1e-11  0.0e+00  2.4e-10  0.0e+00  2.2e-09  1.2e-08
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +226.941
 

end

Visulization of results

In this section, we show the plot of the relation between photovaltics output real power and reactive power (VAR injection). The first plot shows the relation when systme load is 20% of the peak load, the second one shows 30% of the peak load, and the third one shows 40%.

    figure;
    plot(pgs_45,qgs_45,'bo-');
    grid on;
    xlabel('solar real power [MW]');
    ylabel('Optimal inverter VAR injection [MW]');
    title('Optimal inverter reactive power vs power output');

end

Analysis and Conclusions

By choosing appropriate parameters,we obtained results similar to the original paper. However, there are some data which are not announced clearly in paper. In order to make it work, we made some changes, shown as follow:

1) The parameter cv and cr are not given in the paper, we simply set cv=cr=1;

2) The first node(#1)is supposed to be feed from a susbstation,by means of which it's able to maintain a constant voltage value. Thus the load demand of node #1 should be minus. However there is nothing mentioned about the supply in this article.

3) Due to the limitted data access of the simulation, we loose the voltage constraints a little to make CVX feasible.

4)The plot from the visulization part fits the Fig.4 in paper. As for Fig.5, since we cannot access to the value setting of cv and cr, the simulation will not be necessary.

5) Due to the limitation of time, we didn't make the plot more smooth, as the current point number already cost too much times for one simulation(almost two hours).

Published with MATLAB® R2014b