I got 3 different results from 3 solvers:MOSEK,SeDuMi,SDPT3 ,in a code with "rel_entr"

1

Hi, everyone. I got 3 different results from 3 solvers:MOSEK,SeDuMi,SDPT3 ,in a code with “rel_entr”, my code is the following:

N=150;
F=30;
I=6;
b0=10^(-60/10);
Pb=10^(43/10-3);
Pu=10^(23/10-3);
s0=[0,0,0];
s_i=10rand(I,3);
W_backhaul=20;
W_downlink=10;
N0=10^(-174/10);
m=10;
K=100;
r_if=ones(I,F);
vmax=30;
delta=1;
H=80;
q_n=10rand(N,3);
q0=ones(1,3);
b_ifn=ones(I,F,N);
a_ifn=ones(I,F,N);
c_f=zeros(F,1);

cvx_solver mosek
cvx_begin

variables W_backhaul_in(I,N) P_in(I,N) W_downlink_in(I,N) T_n(N) Rdown(I,N);
cnb=log(2)/log(1+b0*Pb./(W_backhaul*N0*sum((s0-q_n).^2,2)));
canshu3=[zeros(N-1,1) eye(N-1);zeros(1,N)]-eye(N);
canshu3(N,N)=0;
canshu=zeros(I,N);
canshu2=zeros(I,N);
canshu4=zeros(I,N);
zkk=0;zkk2=0;
for i=1:I
    for n=1:N
        for f=1:F
            zkk=zkk+b_ifn(i,f,n)*(1-c_f(f,1))*a_ifn(i,f,n);
            zkk2=zkk2+b_ifn(i,f,n)*a_ifn(i,f,n);
        end 
        canshu(i,n)=zkk*log(2)/log(1+b0*Pb./(W_backhaul*N0*sum((s0-q_n(n,:)).^2,2)));zkk=0;
        canshu2(i,n)=zkk2;zkk2=0;
        canshu4(i,n)= 1/sum_square(s_i(i,:)-q_n(n,:));
    end
end
             
minimize(sum(T_n))
subject to
    sum(W_backhaul_in,1)' <= W_backhaul;
    sum(W_downlink_in,1)' <= W_downlink;
    sum(P_in,1)' <= Pu;
   
    T_n >= max( canshu.*inv_pos(W_backhaul_in)   +   canshu2.*      inv_pos(   Rdown   ) *log(2) ,[],1)';
    
    Rdown <= (-1)*rel_entr(W_downlink_in, W_downlink_in+(b0/N0)*canshu4.*P_in)  ;
    
    T_n >= norms(canshu3*q_n,2,2)/vmax;
 
    W_downlink_in >= 0;
    
    P_in >= 0;

cvx_end

Here is Mosek result:

CVX Warning:
Models involving “rel_entr” or other functions in the log, exp, and entropy
family are solved using an experimental successive approximation method.
This method is slower and less reliable than the method CVX employs for
other models. Please see the section of the user’s guide entitled
The successive approximation method
for more details about the approach, and for instructions on how to
suppress this warning message in the future.
警告: 未来的版本中将会删除 NARGCHK。请改用 NARGINCHK 或 NARGOUTCHK。

In exponential (line 17)
In cvx/rel_entr (line 80)
In Untitled (line 55)
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================

Calling Mosek 9.1.9: 26850 variables, 12000 equality constraints
For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

MOSEK warning 710: #2 (nearly) zero elements are specified in sparse col ‘’ (446) of matrix ‘A’.
MOSEK warning 710: #2 (nearly) zero elements are specified in sparse col ‘’ (4331) of matrix ‘A’.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 12000
Cones : 7200
Scalar variables : 26850
Matrix variables : 0
Integer variables : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 2850
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.11
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 12000
Cones : 7200
Scalar variables : 26850
Matrix variables : 0
Integer variables : 0

Optimizer - threads : 2
Optimizer - solved problem : the primal
Optimizer - Constraints : 8999
Optimizer - Cones : 7200
Optimizer - Scalar variables : 23849 conic : 21600
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.03 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 4.06e+04 after factor : 5.82e+04
Factor - dense dim. : 0 flops : 7.70e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.0e+00 1.7e+09 3.0e+03 0.00e+00 3.032780354e+03 3.278035363e+01 1.0e+00 0.23
1 8.2e-01 4.7e+08 1.6e+03 -1.00e+00 2.757776121e+03 -2.395596411e+02 2.7e-01 0.52
2 2.7e-01 1.6e+08 3.5e+02 -1.00e+00 -1.428594517e+03 -2.575055670e+03 9.1e-02 0.56
3 4.1e-02 2.3e+07 1.3e+02 -1.00e+00 -2.588783138e+04 -2.697152885e+04 1.4e-02 0.64
4 1.1e-02 6.5e+06 7.1e+01 -1.00e+00 -9.965173788e+04 -1.005439617e+05 3.8e-03 0.70
5 2.3e-03 1.3e+06 8.0e+01 -1.00e+00 -5.034191265e+05 -5.050081576e+05 7.6e-04 0.72
6 5.9e-04 3.4e+05 4.1e+01 -1.00e+00 -1.945706779e+06 -1.943547583e+06 2.0e-04 0.81
7 1.5e-04 8.3e+04 3.0e+01 -1.00e+00 -7.909354389e+06 -7.893023451e+06 4.9e-05 0.83
8 5.6e-05 3.2e+04 1.8e+01 -1.00e+00 -2.039294953e+07 -2.034399163e+07 1.9e-05 0.86
9 1.3e-05 7.4e+03 8.8e+00 -9.99e-01 -8.899730743e+07 -8.876996540e+07 4.3e-06 0.88
10 3.7e-06 2.1e+03 4.7e+00 -9.97e-01 -3.068829680e+08 -3.060896335e+08 1.2e-06 0.91
Optimizer terminated. Time: 1.03

Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -3.8342208902e+02 nrm: 7e+04 Viol. con: 3e-05 var: 7e+04 cones: 6e-07
Optimizer summary
Optimizer - time: 1.03
Interior-point - iterations : 10 time: 0.92
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00

Status: Infeasible
Optimal value (cvx_optval): +Inf

Here is SDPT3 result:

CVX Warning:
Models involving “rel_entr” or other functions in the log, exp, and entropy
family are solved using an experimental successive approximation method.
This method is slower and less reliable than the method CVX employs for
other models. Please see the section of the user’s guide entitled
The successive approximation method
for more details about the approach, and for instructions on how to
suppress this warning message in the future.
警告: 未来的版本中将会删除 NARGCHK。请改用 NARGINCHK 或 NARGOUTCHK。

In exponential (line 17)
In cvx/rel_entr (line 80)
In Untitled (line 55)
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================

Calling SDPT3 4.0: 26850 variables, 12000 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.

num. of constraints = 12000
dim. of sdp var = 14400, num. of sdp blk = 7200
dim. of linear var = 5250

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|6.9e+02|3.2e+01|4.9e+07| 1.433737e+05 0.000000e+00| 0:0:01| spchol 1 1
1|0.442|0.369|3.8e+02|2.0e+01|3.2e+07| 2.776319e+05 -1.003695e+04| 0:0:02| spchol 1 1
2|0.355|0.222|2.5e+02|1.6e+01|2.9e+07| 5.013593e+05 -2.406821e+04| 0:0:02| spchol 1 1
3|0.541|0.517|1.1e+02|7.7e+00|1.7e+07| 8.372919e+05 -6.217225e+04| 0:0:03| spchol 1 1
4|0.819|0.752|2.1e+01|1.9e+00|5.5e+06| 9.931271e+05 -9.483851e+04| 0:0:03| spchol 1 1
5|0.692|0.966|6.3e+00|7.6e-02|1.2e+06| 6.862235e+05 -8.194823e+04| 0:0:04| spchol 1 1
6|0.881|1.000|7.5e-01|7.8e-03|2.5e+05| 1.747625e+05 -4.151346e+04| 0:0:04| spchol 1 1
7|0.900|0.989|7.5e-02|3.9e-03|2.3e+04| 1.671461e+04 -4.399913e+03| 0:0:04| spchol 1 1
8|0.604|1.000|3.0e-02|8.0e-03|1.6e+04| 1.085278e+04 -2.479579e+03| 0:0:05| spchol 1 1
9|0.895|1.000|3.1e-03|2.2e-03|3.1e+03| 1.674946e+03 -9.299409e+02| 0:0:05| spchol 1 1
10|0.550|0.939|1.4e-03|8.6e-04|2.2e+03| 1.196736e+03 -6.078528e+02| 0:0:06| spchol 1 1
11|0.872|0.984|1.8e-04|3.3e-04|7.7e+02| 1.502621e+02 -5.192416e+02| 0:0:06| spchol 1 1
12|0.501|0.865|9.0e-05|8.8e-05|4.2e+02| 7.320034e+01 -2.829341e+02| 0:0:06| spchol 1 1
13|0.832|0.991|1.5e-05|2.2e-05|1.3e+02|-1.259486e+02 -2.377042e+02| 0:0:07| spchol 1 1
14|0.518|0.982|7.3e-06|4.2e-06|6.3e+01|-1.425211e+02 -1.826220e+02| 0:0:07| spchol 1 1
15|0.619|0.850|2.8e-06|2.3e-06|4.1e+01|-1.483151e+02 -1.735583e+02| 0:0:07| spchol 1 1
16|0.311|0.578|1.9e-06|1.6e-06|3.4e+01|-1.481115e+02 -1.667601e+02| 0:0:08| spchol 1 1
17|0.372|0.551|1.2e-06|1.1e-06|3.0e+01|-1.460661e+02 -1.597056e+02| 0:0:08| spchol 1 1
18|0.436|0.622|6.7e-07|6.6e-07|2.5e+01|-1.429901e+02 -1.542950e+02| 0:0:09| spchol 1 1
19|0.471|0.623|3.6e-07|3.8e-07|1.9e+01|-1.403958e+02 -1.472893e+02| 0:0:09| spchol 1 1
20|0.383|0.553|2.2e-07|2.4e-07|1.7e+01|-1.378068e+02 -1.429672e+02| 0:0:09| spchol 1 1
21|0.368|0.565|1.4e-07|1.5e-07|1.5e+01|-1.351514e+02 -1.379910e+02| 0:0:10| spchol 1 1
22|0.398|0.541|8.4e-08|9.7e-08|1.3e+01|-1.319399e+02 -1.350534e+02| 0:0:10| spchol 1 1
23|0.441|0.575|4.7e-08|5.8e-08|1.1e+01|-1.291054e+02 -1.305398e+02| 0:0:11| spchol 1 1
24|0.411|0.561|2.8e-08|3.5e-08|9.0e+00|-1.264492e+02 -1.270822e+02| 0:0:11| spchol 1 1
25|0.359|0.513|1.8e-08|2.2e-08|8.1e+00|-1.241161e+02 -1.237002e+02| 0:0:12| spchol 1 1
26|0.364|0.473|1.1e-08|1.5e-08|7.6e+00|-1.215947e+02 -1.216146e+02| 0:0:12| spchol 1 1
27|0.440|0.530|6.3e-09|9.4e-09|6.2e+00|-1.189989e+02 -1.184934e+02| 0:0:12| spchol 1 1
28|0.188|0.122|5.1e-09|9.5e-09|6.3e+00|-1.178572e+02 -1.179070e+02| 0:0:13| spchol 1 1
29|0.367|0.154|3.2e-09|9.0e-09|5.9e+00|-1.157997e+02 -1.171110e+02| 0:0:13| spchol 1 1
30|0.472|0.151|1.7e-09|8.4e-09|5.7e+00|-1.134813e+02 -1.161230e+02| 0:0:13| spchol 1 1
31|0.515|0.126|8.3e-10|7.7e-09|5.9e+00|-1.111541e+02 -1.152423e+02| 0:0:14| spchol 1 1
32|0.464|0.127|4.4e-10|7.0e-09|6.1e+00|-1.097651e+02 -1.146128e+02| 0:0:14| spchol 1 1
33|0.493|0.135|2.3e-10|6.3e-09|6.0e+00|-1.090022e+02 -1.142652e+02| 0:0:14| spchol 1 1
34|0.370|0.400|1.4e-10|3.9e-09|5.2e+00|-1.088869e+02 -1.135774e+02| 0:0:15| spchol 1 1
35|0.581|0.561|5.9e-11|1.9e-09|3.8e+00|-1.091639e+02 -1.127028e+02| 0:0:15| spchol 1 1
36|0.468|0.399|3.2e-11|1.2e-09|3.2e+00|-1.093328e+02 -1.123867e+02| 0:0:15| spchol 1 1
37|0.402|0.616|1.9e-11|5.6e-10|2.5e+00|-1.095313e+02 -1.119042e+02| 0:0:16| spchol 1 1
38|0.407|0.488|1.1e-11|3.3e-10|2.1e+00|-1.096685e+02 -1.117400e+02| 0:0:16| spchol 1 1
39|0.489|1.000|5.7e-12|2.2e-12|1.4e+00|-1.098886e+02 -1.113001e+02| 0:0:16| spchol 1 1
40|0.548|0.530|2.6e-12|2.2e-12|1.2e+00|-1.100822e+02 -1.112305e+02| 0:0:17| spchol 1 1
41|0.669|0.844|8.6e-13|1.4e-12|7.7e-01|-1.102853e+02 -1.110455e+02| 0:0:17| spchol 1 1
42|0.851|1.000|1.3e-13|1.0e-12|3.4e-01|-1.105004e+02 -1.108425e+02| 0:0:17| spchol 1 1
43|0.977|0.967|3.0e-14|1.1e-12|1.0e-02|-1.106768e+02 -1.106870e+02| 0:0:18| spchol 1 1
44|1.000|1.000|2.7e-14|1.0e-12|6.2e-04|-1.106810e+02 -1.106816e+02| 0:0:18| spchol 1 1
45|1.000|1.000|2.8e-14|1.0e-12|1.2e-05|-1.106813e+02 -1.106813e+02| 0:0:18| spchol 1 1
46|1.000|1.000|4.3e-14|1.0e-12|4.1e-07|-1.106813e+02 -1.106813e+02| 0:0:19|
stop: max(relative gap, infeasibilities) < 1.49e-08

number of iterations = 46
primal objective value = -1.10681269e+02
dual objective value = -1.10681270e+02
gap := trace(XZ) = 4.12e-07
relative gap = 1.85e-09
actual relative gap = 1.82e-09
rel. primal infeas (scaled problem) = 4.26e-14
rel. dual " " " = 1.04e-12
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 1.1e+02, 7.3e+10, 7.3e+10
norm(A), norm(b), norm© = 8.1e+02, 1.3e+01, 2.8e+02
Total CPU time (secs) = 18.53
CPU time per iteration = 0.40
termination code = 0
DIMACS: 2.8e-13 0.0e+00 1.4e-11 0.0e+00 1.8e-09 1.9e-09

Status: Solved
Optimal value (cvx_optval): +145.458

Here is SeDuMi result:

CVX Warning:
Models involving “rel_entr” or other functions in the log, exp, and entropy
family are solved using an experimental successive approximation method.
This method is slower and less reliable than the method CVX employs for
other models. Please see the section of the user’s guide entitled
The successive approximation method
for more details about the approach, and for instructions on how to
suppress this warning message in the future.
警告: 未来的版本中将会删除 NARGCHK。请改用 NARGINCHK 或 NARGOUTCHK。

In exponential (line 17)
In cvx/rel_entr (line 80)
In Untitled (line 55)
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================

Calling SeDuMi 1.3.4: 26850 variables, 12000 equality constraints
For improved efficiency, SeDuMi is solving the dual problem.

SeDuMi 1.3.4 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 12000, order n = 19651, dim = 26851, blocks = 7201
nnz(A) = 61650 + 0, nnz(ADA) = 104400, nnz(L) = 71100
it : by gap delta rate t/tP t/tD* feas cg cg prec
0 : 1.67E+02 0.000
1 : 7.98E+01 4.41E+01 0.000 0.2643 0.9000 0.9000 7.60 1 1 5.3E+00
2 : -2.53E+01 1.91E+01 0.000 0.4340 0.9000 0.9000 1.17 1 1 2.8E+00
3 : -1.92E+02 1.07E+01 0.000 0.5620 0.9000 0.9000 0.52 1 1 2.2E+00
4 : -7.26E+02 2.76E+00 0.000 0.2573 0.9000 0.9000 0.75 1 1 5.3E-01
5 : -6.90E+02 7.43E-01 0.000 0.2689 0.9000 0.9000 0.65 1 1 1.7E-01
6 : -5.71E+02 2.19E-01 0.000 0.2950 0.9000 0.9000 0.70 1 1 6.5E-02
7 : -4.94E+02 7.64E-02 0.000 0.3486 0.9000 0.9000 0.60 1 1 3.1E-02
8 : -4.52E+02 3.32E-02 0.000 0.4341 0.9000 0.9000 0.53 1 1 1.8E-02
9 : -4.04E+02 1.13E-02 0.000 0.3402 0.9000 0.9000 0.42 1 1 9.9E-03
10 : -3.77E+02 4.78E-03 0.000 0.4238 0.9000 0.9000 0.36 1 1 6.7E-03
11 : -3.40E+02 1.42E-03 0.000 0.2961 0.9000 0.9000 0.27 1 1 4.1E-03
12 : -3.16E+02 4.92E-04 0.000 0.3474 0.9000 0.9000 0.22 1 1 3.0E-03
13 : -2.89E+02 1.38E-04 0.000 0.2806 0.9000 0.9000 0.19 2 2 2.0E-03
14 : -2.69E+02 1.75E-09 0.000 0.0000 0.9000 0.8571 0.17 2 2 2.5E-04
15 : -2.55E+02 7.14E-10 0.000 0.4076 0.9000 0.7862 0.18 5 2 1.5E-04
16 : -2.42E+02 2.81E-10 0.000 0.3932 0.8023 0.9000 0.18 5 5 9.1E-05
17 : -2.29E+02 9.41E-11 0.000 0.3352 0.9000 0.9000 0.17 5 4 4.9E-05
18 : -2.17E+02 3.42E-11 0.000 0.3638 0.9000 0.9000 0.17 4 4 2.8E-05
19 : -2.07E+02 1.24E-11 0.000 0.3625 0.9000 0.9000 0.17 4 4 1.6E-05
20 : -1.97E+02 3.80E-12 0.000 0.3064 0.9000 0.9000 0.15 4 4 8.2E-06
21 : -1.87E+02 1.22E-12 0.000 0.3208 0.9000 0.9000 0.15 4 4 4.4E-06
22 : -1.79E+02 3.74E-13 0.000 0.3064 0.9000 0.9000 0.14 6 6 2.3E-06
23 : -1.72E+02 1.28E-13 0.000 0.3434 0.9000 0.9000 0.14 14 14 1.3E-06
24 : -1.65E+02 4.18E-14 0.000 0.3254 0.9000 0.9000 0.14 13 13 7.1E-07
25 : -1.59E+02 1.46E-14 0.000 0.3489 0.9000 0.9000 0.13 15 15 4.1E-07
26 : -1.54E+02 5.29E-15 0.000 0.3629 0.9000 0.9000 0.13 21 14 2.4E-07
27 : -1.48E+02 1.61E-15 0.000 0.3037 0.9000 0.9000 0.13 16 16 1.2E-07
28 : -1.43E+02 5.61E-16 0.000 0.3495 0.9000 0.9000 0.11 22 16 7.2E-08
29 : -1.39E+02 1.85E-16 0.000 0.3297 0.9000 0.9000 0.12 17 18 3.9E-08
30 : -1.34E+02 5.54E-17 0.000 0.2993 0.9000 0.9000 0.12 26 23 2.0E-08
31 : -1.31E+02 2.00E-17 0.000 0.3608 0.9000 0.9000 0.11 26 26 1.2E-08

iter seconds digits cx by
31 11.3 Inf -1.3078322396e+02 -1.3078267434e+02
|Ax-b| = 3.8e-07, [Ay-c]_+ = 0.0E+00, |x|= 8.1e+01, |y|= 5.3e+08

Detailed timing (sec)
Pre IPM Post
4.610E-01 5.448E+00 5.600E-02
Max-norms: ||b||=1, ||c|| = 2.000000e+01,
Cholesky |add|=300, |skip| = 0, ||L.L|| = 2.63428e+08.

Status: Solved
Optimal value (cvx_optval): +163.94

I don’t know which one to use . And why is Mosek the worst one? Is it that I didn’t call it properly or install it wrong? Is it bad scaling?Thank you for your time.

2

In all cases, CVXQUAD’s Pade approximant has been invoked.

Try removing CVXQUAD’s exponential.m replacement. Then run Mosek in a new MATLAB session. That should utilize Mosek’s native exponential cone capability, which should be the most accurate solution method.

I don’t know what the NARGCHK, NARGINCHK, NARGOUTCHK errors (warnings?) are, but perhaps you mixed use of CVX’s exponential.m with CVXQUAD’s exponential.m in the same MATLAB session? Try a new MATLAB session.

3

Hi Dr Stone. I have replaced it back with the old exponential.m and reopen matlab. Here’s what I got:

CVX Warning:
Models involving “rel_entr” or other functions in the log, exp, and entropy
family are solved using an experimental successive approximation method.
This method is slower and less reliable than the method CVX employs for
other models. Please see the section of the user’s guide entitled
The successive approximation method
for more details about the approach, and for instructions on how to
suppress this warning message in the future.

Calling Mosek 9.1.9: 12600 variables, 6000 equality constraints

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

MOSEK warning 62: The A matrix contains a large value of 1.4e+10 in constraint ‘’ (3301) at variable ‘’ (11701).
MOSEK warning 62: The A matrix contains a large value of 1.5e+10 in constraint ‘’ (3303) at variable ‘’ (11703).
MOSEK warning 62: The A matrix contains a large value of 1.3e+10 in constraint ‘’ (3310) at variable ‘’ (11710).
MOSEK warning 62: The A matrix contains a large value of 3.7e+10 in constraint ‘’ (3316) at variable ‘’ (11716).
MOSEK warning 62: The A matrix contains a large value of 1.3e+10 in constraint ‘’ (3325) at variable ‘’ (11725).
MOSEK warning 62: The A matrix contains a large value of 2.3e+10 in constraint ‘’ (3330) at variable ‘’ (11730).
MOSEK warning 62: The A matrix contains a large value of 1.7e+10 in constraint ‘’ (3340) at variable ‘’ (11740).
MOSEK warning 62: The A matrix contains a large value of 1.5e+10 in constraint ‘’ (3343) at variable ‘’ (11743).
MOSEK warning 62: The A matrix contains a large value of 1.5e+11 in constraint ‘’ (3346) at variable ‘’ (11746).
MOSEK warning 62: The A matrix contains a large value of 6.5e+10 in constraint ‘’ (3349) at variable ‘’ (11749).
Warning number 62 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 6000
Cones : 2700
Scalar variables : 12600
Matrix variables : 0
Integer variables : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 150
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.01
Lin. dep. - number : 0
Presolve terminated. Time: 0.14
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 6000
Cones : 2700
Scalar variables : 12600
Matrix variables : 0
Integer variables : 0

Optimizer - threads : 2
Optimizer - solved problem : the primal
Optimizer - Constraints : 3150
Optimizer - Cones : 2700
Optimizer - Scalar variables : 11400 conic : 8100
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.02 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 1.08e+04 after factor : 1.40e+04
Factor - dense dim. : 0 flops : 1.49e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 7.0e+00 3.2e+01 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.20
1 1.4e+00 6.6e+00 2.4e-01 -4.89e-01 -9.592759056e+02 -9.583904289e+02 2.1e-01 0.48
2 3.5e-01 1.6e+00 3.8e-02 3.45e-01 1.263360446e+03 1.263763324e+03 5.1e-02 0.52
3 1.1e-01 5.1e-01 8.2e-03 6.35e-01 9.497235889e+02 9.499356691e+02 1.6e-02 0.53
4 3.7e-02 1.7e-01 1.8e-03 7.28e-01 9.204018302e+02 9.204973728e+02 5.3e-03 0.56
5 1.3e-02 5.9e-02 5.1e-04 5.57e-01 7.554380706e+02 7.555021069e+02 1.8e-03 0.58
6 5.0e-03 2.3e-02 1.4e-04 6.56e-01 7.040591256e+02 7.040935608e+02 7.2e-04 0.59
7 1.0e-03 4.7e-03 2.4e-05 3.85e-01 5.659820505e+02 5.660066134e+02 1.5e-04 0.61
8 3.8e-04 1.7e-03 8.0e-06 3.99e-01 5.106449156e+02 5.106653917e+02 5.4e-05 0.63
9 1.0e-04 4.7e-04 1.6e-06 4.43e-01 4.555719726e+02 4.555832741e+02 1.5e-05 0.66
10 3.5e-05 1.6e-04 6.4e-07 9.13e-02 4.017522813e+02 4.017679715e+02 5.0e-06 0.67
11 1.0e-05 4.7e-05 1.1e-07 5.95e-01 3.704368248e+02 3.704421444e+02 1.5e-06 0.69
12 4.1e-06 1.9e-05 5.2e-08 5.33e-02 3.390251530e+02 3.390330647e+02 5.8e-07 0.70
13 7.4e-07 3.4e-06 7.2e-09 2.86e-01 3.067996762e+02 3.068043700e+02 1.1e-07 0.72
14 2.8e-07 1.3e-06 3.1e-09 3.88e-02 2.868857807e+02 2.868915291e+02 4.0e-08 0.75
15 8.4e-08 3.8e-07 8.5e-10 1.29e-01 2.655407576e+02 2.655457712e+02 1.2e-08 0.77
16 2.9e-08 1.3e-07 2.6e-10 2.23e-01 2.502605593e+02 2.502644975e+02 4.2e-09 0.78
17 6.1e-09 2.8e-08 5.1e-11 1.68e-01 2.303340143e+02 2.303373841e+02 8.8e-10 0.80
18 2.6e-09 1.2e-08 2.3e-11 1.78e-01 2.196222726e+02 2.196260304e+02 3.8e-10 0.81
19 6.4e-10 2.9e-09 4.4e-12 2.82e-01 2.068078636e+02 2.068102098e+02 9.1e-11 0.83
20 2.5e-10 1.1e-09 2.0e-12 2.58e-02 1.971035377e+02 1.971066548e+02 3.6e-11 0.84
21 7.9e-11 3.6e-10 5.2e-13 2.27e-01 1.880737094e+02 1.880757889e+02 1.1e-11 0.86
22 2.1e-11 9.7e-11 1.4e-13 1.45e-01 1.783992778e+02 1.784013112e+02 3.0e-12 0.89
23 9.2e-12 4.2e-11 5.7e-14 2.07e-01 1.728417151e+02 1.728435957e+02 1.3e-12 0.92
24 1.7e-12 7.9e-12 1.0e-14 1.40e-01 1.632088035e+02 1.632104239e+02 2.5e-13 0.94
25 7.1e-13 3.3e-12 4.5e-15 1.07e-01 1.576732208e+02 1.576751920e+02 1.0e-13 0.97
26 2.0e-13 9.0e-13 9.9e-16 2.73e-01 1.516916848e+02 1.516929197e+02 2.8e-14 0.98
27 9.2e-14 4.2e-13 5.2e-16 2.88e-02 1.476152572e+02 1.476168313e+02 1.3e-14 1.00
28 1.7e-14 7.8e-14 8.5e-17 1.25e-01 1.405612710e+02 1.405624792e+02 2.4e-15 1.01
29 6.2e-15 2.8e-14 3.6e-17 8.39e-02 1.356047799e+02 1.356064601e+02 8.9e-16 1.03
30 2.2e-15 1.0e-14 8.3e-18 6.03e-01 1.324491001e+02 1.324497812e+02 3.2e-16 1.05
31 9.5e-16 4.3e-15 4.6e-18 -2.02e-02 1.284249797e+02 1.284261377e+02 1.4e-16 1.06
32 2.0e-16 9.7e-16 7.3e-19 2.64e-01 1.241010205e+02 1.241016632e+02 2.9e-17 1.08
33 6.8e-17 6.5e-16 2.9e-19 -2.02e-02 1.202352266e+02 1.202361379e+02 9.7e-18 1.09
34 3.8e-17 4.0e-16 1.5e-19 1.88e-01 1.185191277e+02 1.185199084e+02 5.4e-18 1.11
35 2.0e-17 2.2e-16 7.1e-20 2.08e-01 1.167308396e+02 1.167314834e+02 2.9e-18 1.13
36 1.2e-17 1.3e-16 3.7e-20 3.11e-01 1.154130313e+02 1.154135323e+02 1.7e-18 1.14
37 7.7e-18 8.4e-17 2.1e-20 4.93e-01 1.145473121e+02 1.145476826e+02 1.1e-18 1.16
38 4.7e-18 5.0e-17 1.1e-20 6.20e-01 1.137974734e+02 1.137977294e+02 6.8e-19 1.17
39 1.5e-18 4.1e-17 2.3e-21 6.74e-01 1.127584895e+02 1.127585986e+02 2.2e-19 1.19
40 1.3e-18 4.5e-17 1.7e-21 7.73e-01 1.126577701e+02 1.126578686e+02 1.8e-19 1.20
41 5.6e-19 7.9e-17 6.0e-22 7.84e-01 1.123425980e+02 1.123426516e+02 8.0e-20 1.22
42 5.2e-19 8.5e-17 4.0e-22 7.99e-01 1.123129368e+02 1.123129875e+02 7.2e-20 1.23
43 6.2e-19 1.4e-16 4.1e-22 8.12e-01 1.122124609e+02 1.122124969e+02 4.6e-20 1.25
44 2.2e-18 2.0e-16 1.7e-22 8.49e-01 1.121048640e+02 1.121048822e+02 2.0e-20 1.26
45 1.9e-18 3.2e-16 3.2e-23 8.62e-01 1.120870821e+02 1.120870978e+02 1.6e-20 1.28
46 2.9e-18 5.7e-16 5.2e-23 8.76e-01 1.120400083e+02 1.120400160e+02 7.0e-21 1.30
Optimizer terminated. Time: 1.52

Interior-point solution summary
Problem status : ILL_POSED
Solution status : DUAL_ILLPOSED_CER
Primal. obj: 3.0376183549e-06 nrm: 3e+02 Viol. con: 5e-07 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 1.52
Interior-point - iterations : 46 time: 1.31
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00

Status: Failed
Optimal value (cvx_optval): NaN

By the way, NARGCHK, NARGINCHK, NARGOUTCHK warnings I posted previously means “we will remove NARGCHK in future edition, please use NARGINCHK or NARGOUTCHK instead”.

4

These

MOSEK warning 62: The A matrix contains a large value of 1.4e+10 in constraint ‘’ (3301) at variable ‘’ (11701).

MOSEK warnings tells you that the model is badly scaled. Such large numbers in A indicates you have a bad model you are likely to have hard time solving reliably.

5

Hi! Mr Andersen. Thank you for your help. I get it now but in communication area SNR(signal-noise ratio) can be as big as 1.4e+10, then shannon capacity= log(1+SNR)=just a few bits. Maybe I should change unit. Mosek work very well and fast on other code.Thank you for your work!!!

7

I have installed the CVXQUAD’s exponential.m function in my cvx. If I use the mosek solver, as you said, the CVXQUAD’s exponential.m should be removed, right?

8

Yes, Swap back in the original exponential.m which came wit the CVX distribution.

9

How did you do the scaling?

10

Read https://docs.mosek.com/modeling-cookbook/practical.html?highlight=scaling#scaling