Why CVX 2.1 code cannot work in CVX 3.0？

Dayao · November 9, 2018, 4:35am

My CVX code is as follows:

function  etaa = OMA_itera_SumRate(BETAA, Gammaa, Phii, etaa_former, M, K, N, Pd)
cauy_former = etaa_former.^0.5;
Rate_former = OMA_conven_DL_CF_Rate( BETAA,Gammaa,Phii,etaa_former,M,K,N,Pd ) ;
SINR_former = 2.^Rate_former - 1;

a = zeros(K,1); % nominator of SINR
for k=1:K
        a(k) = ( sum( cauy_former(:,k) .* (Gammaa(:,k).^0.5) ))^2; 
end
b = a ./ SINR_former; % denominator of SINR

%% CVX
cvx_begin

variable t(K)
variable rou(K,K)
variable V(M) nonnegative
variable cauy(M,K)

sb1_left =  cvx(zeros(K,1));
sb1_right = cvx(zeros(K,1));
sb2_left =  cvx(zeros(M,1));
sb3_left =  cvx(zeros(K,K));

%% subject 1
for k=1:K
   I = eye(K);
   I(:,k)=[];
   vk1 = (Phii'*Phii(:,k).*rou(:,k)).'*I;
   vk2 = 1/(N^0.5) * ((BETAA(:,k).^(1/2)).*V).';
   vk3 = 1/(Pd^0.5 * N);
   
   W = [vk1 vk2 vk3];  %行向量
        
   sb1_left(k) = SINR_former(k) / ( 1+SINR_former(k) ) / b(k) * sum(W .* W);
   
   sb1_right(k) = log( 1 + SINR_former(k)) + SINR_former(k) / ( 1+SINR_former(k) ) *  ...
                    ( 2 - sqrt(a(k)) * inv_pos( 2 * sum( cauy(:,k) .* (Gammaa(:,k).^0.5) )  - sqrt(a(k)) ) ) - t(k);
end


%% -----------------------------subject 2

for m=1:M
   sb2_left(m) = norm(  cauy(m,:).' );
end

%% -----------------------------subject 3

for k=1:K
    for kk=[1:k-1,k+1:K]
        sb3_left(kk,k) = sum( (Gammaa(:,kk).^0.5) ./ BETAA(:,kk) .* cauy(:,kk) .* BETAA(:,k) );
    end
end

maximize 1/log(2) * sum(t(:))

%% -----------------------------subject------------------------------
subject to

    for k=1:K
        sb1_left(k) - sb1_right(k) <= 0;
    end
    
    for m=1:M
          sb2_left(m) - V(m) <=  0 ;
    end
    
    for k=1:K
        for kk=[1:k-1,k+1:K]
           sb3_left(kk,k) - rou(kk,k) <= 0;
        end
    end
    
    for m=1:M  % 总功率约束
       0 <= V(m) <= 1/sqrt(N);
    end
    
    for m=1:M
        for k=1:K
            -cauy(m,k) <= 0;
        end
    end
    
    for k=1:K  % 引入的分母大于0
        sum( cauy_former(:,k) .* (Gammaa(:,k).^0.5) ) - 2 * sum( cauy(:,k) .* (Gammaa(:,k).^0.5) ) <= 0;
    end


cvx_end
etaa = cauy.^2;

end

Since my code needs a few iterations to converge. I only give one iteration result:
When using CVX 3.0 and SDPT3:

Calling SDPT3 4.0: 5734 variables, 2478 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 2478
 dim. of socp   var  = 4374,   num. of socp blk  = 1218
 dim. of linear var  = 1340
 dim. of free   var  = 20
 *** convert ublk to linear blk
********************************************************************************************
   SDPT3: homogeneous self-dual path-following algorithms
********************************************************************************************
 version  predcorr  gam  expon
    NT      1      0.000   1
it pstep dstep pinfeas dinfeas  gap     mean(obj)    cputime    kap   tau    theta
--------------------------------------------------------------------------------------------
 0|0.000|0.000|1.3e+03|6.2e+02|5.7e+17| 1.691623e+14| 0:0:00|5.7e+18|1.0e+00|1.0e+00| spchol
  SMW too ill-conditioned, switch to LU factor, 2.5e+35.
  switch to LU factor splu  1   1
 1|0.000|0.000|1.3e+03|6.2e+02|5.7e+17| 1.643769e+14| 0:0:00|5.7e+18|1.0e+00|1.0e+00| splu  1   1
 2|0.000|0.000|1.3e+03|6.2e+02|5.7e+17| 1.561949e+14| 0:0:00|5.7e+18|1.0e+00|1.0e+00| splu  1   1
 3|0.000|0.000|1.3e+03|6.2e+02|5.7e+17| 1.228457e+14| 0:0:01|5.7e+18|1.0e+00|1.0e+00| splu  1   1
 4|0.001|0.001|1.3e+03|6.2e+02|5.7e+17| 1.817396e+13| 0:0:01|5.6e+18|1.0e+00|1.0e+00| splu  1   1
 5|0.004|0.004|1.3e+03|6.2e+02|5.8e+17|-2.958569e+14| 0:0:01|5.6e+18|1.0e+00|1.0e+00| splu  1   1
 6|0.012|0.012|1.3e+03|6.2e+02|6.1e+17|-1.269515e+15| 0:0:01|5.6e+18|9.9e-01|9.9e-01| splu  1   1
 7|0.036|0.036|1.3e+03|6.1e+02|6.9e+17|-4.058228e+15| 0:0:01|5.5e+18|9.8e-01|9.7e-01| splu  1   1
 8|0.116|0.116|1.2e+03|5.9e+02|9.2e+17|-1.233647e+16| 0:0:01|5.0e+18|9.4e-01|9.0e-01| splu  1   1
 9|0.314|0.314|1.0e+03|5.0e+02|1.3e+18|-3.109399e+16| 0:0:01|3.9e+18|8.6e-01|7.0e-01| splu  1   1
10|0.677|0.677|5.4e+02|2.6e+02|1.2e+18|-4.830574e+16| 0:0:01|1.7e+18|7.6e-01|3.2e-01| splu  1   1
11|0.955|0.955|3.7e+01|1.8e+01|1.2e+17|-6.825671e+15| 0:0:01|5.3e+16|7.7e-01|2.2e-02| splu  1   1
12|0.866|0.866|4.8e+00|2.3e+00|1.5e+16| 8.504199e+14| 0:0:01|1.0e+15|8.6e-01|3.2e-03| splu  1   1
13|0.867|0.867|6.4e-01|3.1e-01|1.8e+15| 3.426609e+14| 0:0:01|2.0e+13|9.6e-01|4.8e-04| splu  1   1
14|0.901|0.901|6.2e-02|3.0e-02|1.7e+14| 3.783320e+13| 0:0:02|1.0e+12|1.0e+00|4.9e-05| splu  1   1
15|0.863|0.863|1.7e-02|8.1e-03|6.2e+13| 1.295577e+13| 0:0:02|1.8e+11|1.0e+00|1.3e-05| splu  1   1
16|1.000|1.000|2.6e-03|1.7e-03|1.2e+13| 2.476994e+12| 0:0:02|1.3e+10|1.0e+00|2.0e-06| splu  1   1
17|0.932|0.932|2.1e-04|1.2e-03|1.0e+12| 1.992965e+11| 0:0:02|2.9e+09|1.0e+00|1.6e-07| splu  1   1
18|0.914|0.914|3.1e-05|9.1e-04|1.5e+11| 3.042284e+10| 0:0:02|4.2e+08|9.9e-01|2.4e-08| splu  1   1
19|0.976|0.976|2.9e-06|8.0e-04|1.4e+10| 2.925110e+09| 0:0:02|3.7e+07|9.9e-01|2.3e-09| splu  1   1
20|0.977|0.977|7.3e-08|7.1e-04|3.5e+08| 7.059321e+07| 0:0:02|3.2e+06|9.9e-01|5.6e-11| splu  1   1
21|0.801|0.801|2.8e-08|2.0e-04|1.4e+08| 2.709181e+07| 0:0:02|7.6e+05|9.7e-01|2.1e-11| splu  1   1
22|0.520|0.520|1.9e-08|9.9e-05|9.4e+07| 1.775422e+07| 0:0:03|3.9e+05|9.5e-01|1.4e-11| splu  1   1
23|0.467|0.467|2.0e-08|5.4e-05|6.5e+07| 1.195336e+07| 0:0:03|2.2e+05|9.4e-01|9.2e-12| splu  1   1
24|0.555|0.555|4.2e-08|2.4e-05|4.4e+07| 7.771764e+06| 0:0:03|1.1e+05|9.2e-01|5.9e-12| splu  1   1
25|0.467|0.467|1.1e-07|1.3e-05|3.1e+07| 5.337909e+06| 0:0:03|6.3e+04|9.1e-01|4.0e-12| splu  1   1
26|0.834|0.834|3.7e-07|2.2e-06|1.2e+07| 2.161637e+06| 0:0:03|1.5e+04|8.9e-01|1.6e-12| splu  1   1
27|0.771|0.771|9.6e-08|5.1e-07|4.3e+06| 7.458550e+05| 0:0:04|5.1e+03|8.9e-01|5.5e-13| splu  1   1
28|0.652|0.652|3.5e-08|1.8e-07|2.2e+06| 3.672824e+05| 0:0:04|2.2e+03|8.9e-01|2.7e-13| splu  1   1
29|0.924|0.924|2.8e-09|1.8e-08|2.9e+05| 4.452459e+04| 0:0:04|4.8e+02|8.9e-01|3.4e-14| splu  1   1
30|0.984|0.984|1.9e-09|4.5e-10|5.2e+03| 6.009354e+02| 0:0:04|5.1e+01|8.9e-01|5.6e-16| splu  1   1
31|0.885|0.885|2.5e-08|7.7e-11|6.6e+02| 3.630579e+01| 0:0:04|6.5e+00|9.0e-01|6.6e-17| splu  1   2
32|0.343|0.343|3.2e-07|7.3e-11|5.7e+02| 2.783975e+01| 0:0:04|4.3e+00|8.9e-01|5.4e-17| splu  2   2
33|0.572|0.572|3.7e-07|5.2e-11|3.7e+02| 1.024168e+01| 0:0:04|1.9e+00|8.9e-01|3.5e-17| splu  2   2
34|0.574|0.574|6.5e-07|3.2e-11|2.5e+02| 4.709546e-01| 0:0:05|8.5e-01|8.9e-01|2.3e-17| splu  2   2
35|0.733|0.733|1.0e-06|2.6e-11|1.3e+02|-8.352167e+00| 0:0:05|2.6e-01|8.9e-01|1.3e-17| splu  2   3
36|0.692|0.692|2.7e-06|2.2e-11|7.1e+01|-1.298662e+01| 0:0:05|9.4e-02|8.8e-01|7.0e-18| splu  3   4
37|0.656|0.656|1.8e-06|2.3e-11|4.0e+01|-1.532888e+01| 0:0:05|4.0e-02|8.8e-01|3.8e-18| splu  3   4
38|0.826|0.826|3.5e-07|2.3e-11|1.6e+01|-1.685203e+01| 0:0:05|1.2e-02|8.8e-01|1.7e-18| splu  4   3
39|0.842|0.842|1.2e-05|1.8e-11|6.5e+00|-1.741724e+01| 0:0:06|4.0e-03|8.8e-01|6.8e-19| splu  5   5
40|0.886|0.886|3.9e-05|1.8e-11|2.4e+00|-1.771171e+01| 0:0:06|1.4e-03|8.8e-01|2.6e-19| splu  5   7
41|0.934|0.934|5.1e-05|2.4e-11|8.5e-01|-1.791364e+01| 0:0:06|4.3e-04|8.8e-01|9.5e-20| splu ^ 8   8
42|0.953|0.953|5.2e-05|2.2e-11|2.1e-01|-1.816252e+01| 0:0:06|1.4e-04|8.8e-01|2.3e-20| splu  8  13
  stop: X, Z not both positive definite
43|0.158|0.506|5.2e-05|2.2e-11|2.1e-01|-1.816252e+01| 0:0:06|1.4e-04|8.8e-01|2.3e-20|
-------------------------------------------------------------------
 number of iterations   = 43
 primal objective value = -1.85013768e+01
 dual   objective value = -1.78236583e+01
 gap := trace(XZ)       = 2.06e-01
 relative gap           = 1.07e-02
 actual relative gap    = -1.82e-02
 rel. primal infeas     = 5.22e-05
 rel. dual   infeas     = 2.24e-11
 norm(X), norm(y), norm(Z) = 3.3e+12, 5.0e+05, 5.0e+05
 norm(A), norm(b), norm(C) = 1.5e+03, 3.3e+12, 1.8e+01
 Total CPU time (secs)  = 6.47  
 CPU time per iteration = 0.15  
 termination code       = -3
 DIMACS: 5.2e-05  0.0e+00  2.2e-11  0.0e+00  -1.8e-02  5.5e-03
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Failed
Optimal value (cvx_optval): NaN

However, when I use CVX 2.1 and SDPT3 solver:

Calling SDPT3 4.0: 5752 variables, 2436 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 2436
 dim. of sdp    var  = 2376,   num. of sdp  blk  = 1188
 dim. of socp   var  = 840,   num. of socp blk  = 40
 dim. of linear var  = 1348
*******************************************************************
   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|1.2e+02|4.0e+01|4.9e+17| 8.104497e+14  0.000000e+00| 0:0:00| spchol  2  2 
 1|0.145|0.049|9.9e+01|3.8e+01|5.2e+17| 2.715423e+15 -7.314595e+14| 0:0:01| spchol  2  2 
 2|0.948|0.578|5.1e+00|1.6e+01|2.1e+17| 8.007610e+15 -5.024198e+15| 0:0:01| spchol  2  2 
 3|0.948|0.987|2.7e-01|3.2e-01|9.7e+15| 5.346625e+15 -5.253429e+14| 0:0:01| spchol  2  2 
 4|0.537|1.000|1.2e-01|6.3e-02|4.4e+15| 3.060982e+15 -6.128998e+14| 0:0:01| spchol  2  2 
 5|0.964|1.000|4.5e-03|3.1e-02|3.5e+14| 2.409214e+14 -7.318205e+13| 0:0:01| spchol  2  2 
 6|0.927|0.986|3.3e-04|1.7e-02|2.3e+13| 1.891615e+13 -6.967979e+11| 0:0:01| spchol  2  2 
 7|0.758|1.000|7.9e-05|7.9e-03|1.0e+13| 7.412725e+12 -1.761701e+12| 0:0:01| spchol  2  2 
 8|0.983|0.985|1.4e-06|4.0e-03|2.0e+11| 1.356173e+11  1.406349e+11| 0:0:01| spchol  2  2 
 9|0.634|1.000|5.0e-07|2.0e-03|9.0e+10| 6.569678e+10  7.182319e+10| 0:0:01| spchol  2  2 
10|0.914|1.000|4.3e-08|9.8e-04|3.0e+10| 1.971580e+10  3.474824e+10| 0:0:01| spchol  2  2 
11|0.902|0.986|4.2e-09|5.0e-04|2.3e+09| 1.911298e+09  2.171653e+10| 0:0:02| spchol  2  2 
12|0.749|1.000|1.0e-09|2.4e-04|1.3e+09| 8.981232e+08  1.046914e+10| 0:0:02| spchol  2  2 
13|0.952|0.984|5.1e-11|1.2e-04|5.7e+07| 4.472972e+07  5.462067e+09| 0:0:02| spchol  2  2 
14|0.731|1.000|1.4e-11|6.1e-05|3.3e+07| 2.269493e+07  2.683394e+09| 0:0:02| spchol  2  2 
15|0.921|0.993|1.1e-12|3.1e-05|2.5e+06| 2.054479e+06  1.354173e+09| 0:0:02| spchol  2  2 
16|0.843|1.000|9.8e-13|1.5e-05|1.2e+06| 8.408977e+05  6.724280e+08| 0:0:02| spchol  2  2 
17|0.883|1.000|3.2e-13|7.6e-06|1.7e+05| 1.396003e+05  3.363512e+08| 0:0:02| spchol  2  2 
18|0.959|1.000|2.4e-12|3.8e-06|2.4e+04| 1.709653e+04  1.681815e+08| 0:0:02| spchol  2  2 
19|0.963|0.983|5.3e-12|1.9e-06|8.5e+02| 6.321196e+02  8.552738e+07| 0:0:02| spchol  2  2 
20|0.730|1.000|8.5e-11|1.8e-12|4.1e+02| 2.549828e+02 -1.127586e+02| 0:0:02| spchol  2  2 
21|0.505|0.585|4.2e-11|1.1e-07|3.5e+02| 1.820902e+02  4.921447e+06| 0:0:02| spchol  2  2 
22|0.943|0.956|1.0e-11|4.9e-09|1.5e+02| 6.426815e+01  2.141988e+05| 0:0:02|
  lack of progress in infeas
-------------------------------------------------------------------
 number of iterations   = 22
 primal objective value =  6.32119593e+02
 dual   objective value =  8.55273781e+07
 gap := trace(XZ)       = 8.51e+02
 relative gap           = 9.95e-06
 actual relative gap    = -1.00e+00
 rel. primal infeas (scaled problem)   = 5.31e-12
 rel. dual     "        "       "      = 1.94e-06
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 3.0e+12, 8.1e+05, 8.1e+05
 norm(A), norm(b), norm(C) = 5.9e+01, 3.0e+12, 3.6e+01
 Total CPU time (secs)  = 2.31  
 CPU time per iteration = 0.11  
 termination code       =  0
 DIMACS: 6.0e-11  0.0e+00  3.5e-05  0.0e+00  -1.0e+00  9.9e-06
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +8.55274e+07

What it is so and how to deal with this?

In addition, since the scale of the problem is large, I also considered the SCS solver for CVX 3.0. However, it still doesnot work:

Calling SCS 2.0.2: 5746 variables, 2482 equality constraints
   For improved efficiency, SCS is solving the dual problem.
------------------------------------------------------------
WARN: A->p (column pointers) not strictly increasing, column 0 empty
ERROR: A->p (column pointers) decreasing
invalid linear system input data
ERROR: Validation returned failure
Failure:could not initialize work
------------------------------------------------------------
Status: Failed
Optimal value (cvx_optval): NaN

Mark_L_Stone · November 9, 2018, 4:45am

CVX 3.0beta has numerous serious bugs. Therefore, we can’t be confident the solver is being provided the correct problem formulation by CVX 3.0beta. There are numerous example of problems run under CVX 3.0beta in which the solver and CVX declared optimality, but the solution clearly violated one or more constraints in the problem (I’m not talking about solutions which are within solver tolerance of being feasible). Use ECOS under CVX3.0beta only if you like failure or getting the wrong answer.

I have no idea whether that is happening in your case.

Use CVX 3.0beta at your own peril.

Dayao · November 9, 2018, 4:51am

Thanks Stone. I have been using CVX 2.1 all the time. However, the large scale of my problem takes a long time to determine, even one day. Hence I installed SCS solver. The SCS solver only is accepted by CVX 3.0. Thanks for your advice.

Mark_L_Stone · November 9, 2018, 5:01am

You should expewct SCS to be much slower than second order solvers such as Mosek, SDPT3, and SeDuMii. The only reasons to use SCS would be1) if you don;t have enough memory to run a second order solve, i.e., a large problem or 2) to use native exponential cone capability of SCS.

I haven’t looked very carefully at your program, but am confused. It appears your program involves log(cvx_expression), which means that either 1) it is being solved by SCS or ECOS using native exponential cone capability (doesn’t explain your SDPT3 output) or 2) CVX’s successive approximation method is used, but your output doesn’t look like that method is used or 3) CVXQUAD is being used, but that wouldn’t be invoked unless your problem werereformulated to not explicitly use log, and the Using Pade approximation message isn;t shown (unless you cut that out)… CVXQUAD: How to use CVXQUAD’s Pade Approximant instead of CVX’s unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD’s Quantum (Matrix) Entropy & Matrix Log related functions

What are the iterations you are referring to?

Dayao · November 9, 2018, 5:11am

Thanks for your answer. You are right, my program involves log(cvx_expression). It is hard to find a global optimal solution since it is nonconvex. I used the sequential convex approximation (SCA) to find a sub-optimal solution. It needs a few iteration to converge. I have already installed CVXQUAD, and the result is obtained by using CVXQUAD.

Mark_L_Stone · November 9, 2018, 5:14am

I have seen bugs with use of CVXQUAD under CVX 3.0beta. As I stated in the linked CVXQUAD thread

Note: CVX 3.0beta is not really recommended to anyone due to its numerous bugs. It is strongly recommended to not use CVXQUAD with CVX 3.0beta. Please use CVX 2.1 instead.

Even if it ran correctly, SCS will be much slower than SDPT3 or SeDuMi.

Dayao · November 9, 2018, 5:14am

You mentiond the output, I also think it is weird. However, When I run this program multiple times, there will always be a large output. Please see:

Calling SDPT3 4.0: 3112 variables, 1284 equality constraints
   For improved efficiency, SDPT3 is solving the dual problem.
------------------------------------------------------------

 num. of constraints = 1284
 dim. of sdp    var  = 1216,   num. of sdp  blk  = 608
 dim. of socp   var  = 520,   num. of socp blk  = 40
 dim. of linear var  = 768
*******************************************************************
   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|7.6e+01|3.2e+01|8.4e+17| 2.392294e+15  0.000000e+00| 0:0:00| spchol  2  2 
 1|0.237|0.080|5.8e+01|3.0e+01|9.2e+17| 7.613543e+15 -1.580352e+15| 0:0:00| spchol  2  2 
 2|0.763|0.708|1.4e+01|8.8e+00|3.5e+17| 1.673233e+16 -1.036945e+16| 0:0:00| spchol  2  2 
 3|0.944|0.911|7.8e-01|8.9e-01|5.6e+16| 1.614821e+16 -7.587125e+15| 0:0:01| spchol  2  2 
 4|0.898|0.893|7.9e-02|1.5e-01|9.1e+15| 4.451670e+15 -1.375918e+15| 0:0:01| spchol  2  2 
 5|0.730|1.000|2.1e-02|3.1e-02|4.7e+15| 2.966150e+15 -1.206454e+15| 0:0:01| spchol  2  2 
 6|0.949|0.950|1.1e-03|2.1e-02|6.0e+14| 3.794632e+14 -1.723338e+14| 0:0:01| spchol  2  2 
 7|0.958|1.000|4.6e-05|8.0e-03|1.2e+14| 8.412482e+13 -3.526067e+13| 0:0:01| spchol  2  2 
 8|0.956|0.952|2.0e-06|4.1e-03|2.6e+13| 1.683833e+13 -7.656260e+12| 0:0:01| spchol  2  2 
 9|0.878|1.000|2.5e-07|2.0e-03|4.9e+12| 3.787868e+12 -7.802017e+11| 0:0:01| spchol  2  2 
10|0.766|0.989|5.8e-08|9.9e-04|2.0e+12| 1.557089e+12 -3.379577e+11| 0:0:01| spchol  2  2 
11|0.948|1.000|3.0e-09|4.9e-04|2.5e+11| 1.908371e+11 -1.000599e+10| 0:0:01| spchol  2  2 
12|0.902|0.992|2.9e-10|2.5e-04|4.1e+10| 3.242019e+10  1.584304e+10| 0:0:01| spchol  2  2 
13|0.776|1.000|6.5e-11|1.2e-04|1.6e+10| 1.218296e+10  8.591759e+09| 0:0:01| spchol  2  2 
14|0.950|0.938|3.2e-12|6.5e-05|1.7e+09| 1.147032e+09  5.778794e+09| 0:0:01| spchol  2  2 
15|0.816|1.000|6.0e-13|3.1e-05|6.8e+08| 4.942068e+08  2.766821e+09| 0:0:01| spchol  2  2 
16|0.924|0.976|4.6e-14|1.6e-05|9.2e+07| 6.925850e+07  1.480842e+09| 0:0:01| spchol  2  2 
17|0.860|1.000|2.8e-14|7.6e-06|2.4e+07| 1.816064e+07  7.275704e+08| 0:0:01| spchol  2  2 
18|0.877|0.982|3.8e-14|3.9e-06|6.4e+06| 4.863165e+06  3.712833e+08| 0:0:01| spchol  2  2 
19|0.912|0.993|9.0e-14|1.9e-06|8.4e+05| 6.803954e+05  1.842802e+08| 0:0:01| spchol  2  2 
20|0.954|1.000|8.1e-13|1.9e-07|2.5e+05| 1.771776e+05  1.823998e+07| 0:0:01| spchol  2  2 
21|0.952|0.939|1.5e-13|3.0e-08|2.6e+04| 1.703298e+04  2.827859e+06| 0:0:01| spchol  2  2 
22|0.959|1.000|2.7e-13|2.4e-09|5.6e+03| 3.779837e+03  1.814047e+05| 0:0:01| spchol  2  2 
23|0.953|1.000|5.2e-14|4.0e-09|1.9e+03| 1.186766e+03  1.766519e+04| 0:0:01| spchol  2  2 
24|0.949|1.000|1.2e-14|1.8e-08|7.2e+02| 3.847381e+02  1.566441e+03| 0:0:01| spchol  2  2 
25|1.000|1.000|2.4e-15|2.1e-12|2.9e+02| 1.208085e+02  4.196885e+01| 0:0:01| spchol  2  2 
26|0.984|0.877|6.3e-16|5.4e-13|1.3e+02| 2.444593e+01 -4.928760e+01| 0:0:01| spchol  2  2 
27|1.000|0.938|3.1e-16|1.0e-13|5.3e+01|-1.090574e+01 -5.424652e+01| 0:0:01| spchol  2  2 
28|1.000|1.000|1.8e-16|2.0e-14|2.0e+01|-2.709181e+01 -4.509241e+01| 0:0:01| spchol  2  2 
29|1.000|0.962|1.9e-16|8.2e-15|7.8e+00|-3.334692e+01 -4.036626e+01| 0:0:01| spchol  2  2 
30|0.972|1.000|1.6e-16|3.0e-15|3.2e+00|-3.550440e+01 -3.843061e+01| 0:0:02| spchol  2  2 
31|1.000|1.000|2.0e-16|1.1e-15|1.1e+00|-3.654109e+01 -3.756140e+01| 0:0:02| spchol  2  2 
32|0.967|1.000|1.9e-16|2.9e-16|2.6e-01|-3.694995e+01 -3.718478e+01| 0:0:02| spchol  2  2 
33|1.000|1.000|3.2e-16|7.1e-17|8.7e-02|-3.703727e+01 -3.711651e+01| 0:0:02| spchol  2  2 
34|0.979|0.973|4.4e-16|1.9e-17|1.5e-02|-3.707098e+01 -3.708469e+01| 0:0:02| spchol  2  2 
35|1.000|1.000|6.0e-16|1.0e-17|6.4e-03|-3.707494e+01 -3.708075e+01| 0:0:02| spchol  2  2 
36|0.941|0.939|7.4e-16|1.0e-17|7.4e-04|-3.707757e+01 -3.707821e+01| 0:0:02| spchol  2  2 
37|1.000|1.000|8.8e-16|1.0e-17|2.4e-04|-3.707778e+01 -3.707800e+01| 0:0:02| spchol  2  2 
38|1.000|0.996|1.1e-15|1.1e-17|3.1e-05|-3.707788e+01 -3.707791e+01| 0:0:02|
  stop: max(relative gap, infeasibilities) < 1.35e-06
-------------------------------------------------------------------
 number of iterations   = 38
 primal objective value = -3.70778778e+01
 dual   objective value = -3.70779055e+01
 gap := trace(XZ)       = 3.06e-05
 relative gap           = 4.08e-07
 actual relative gap    = 3.70e-07
 rel. primal infeas (scaled problem)   = 1.12e-15
 rel. dual     "        "       "      = 1.11e-17
 rel. primal infeas (unscaled problem) = 0.00e+00
 rel. dual     "        "       "      = 0.00e+00
 norm(X), norm(y), norm(Z) = 1.3e+13, 5.8e+07, 5.8e+07
 norm(A), norm(b), norm(C) = 4.5e+01, 1.3e+13, 2.6e+01
 Total CPU time (secs)  = 1.78  
 CPU time per iteration = 0.05  
 termination code       =  0
 DIMACS: 1.1e-14  0.0e+00  1.4e-16  0.0e+00  3.7e-07  4.1e-07
-------------------------------------------------------------------
 
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +24.104

Mark_L_Stone · November 9, 2018, 5:17am

I don;t understand what you find weird. What are you trying to bring to my attention?

Dayao · November 9, 2018, 5:20am

Nothing. Thank you for solving my previous confusion, thank you！

Mark_L_Stone · November 9, 2018, 5:44am

Did your program, exactly as shown, run and produce that output using CVXQUAD? As far as I know, explicit use of log will not result in CVXQUAD’s Pade approximation being used instead of CVX’s successive approximation method. Did you actually run different code, using either -rel_entr(1,cvx_expression) or adding a variable and using explicit exponential cone construct?

Dayao · November 9, 2018, 6:53am

Sorry, Mark. You are right. I think CVXQUAD is not worked in my program. I will reinstall CVXQUAD and check the result again.

Mark_L_Stone · November 9, 2018, 7:05am

Follow the instructions in CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions including the required reformulation of your program, which is quite simple for log.