Dear Mark,
CVX: Software for Disciplined Convex Programming ©2014 CVX Research
Version 2.1, Build 1123 (cff5298) Sun Dec 17 18:58:10 2017
---------------------------------------------------------------------------
Installation info:
Path: C:\Program Files\MATLAB\R2017a\cvx
MATLAB version: 9.2 (R2017a)
OS: Windows 7 amd64 version 6.1
Java version: 1.7.0_60
Verfying CVX directory contents:
WARNING: The following extra files/directories were found:
C:\Program Files\MATLAB\R2017a\cvx\cvxquad-master\ + 18 files, 2 subdirectories
These files may alter the behavior of CVX in unsupported ways.
Preferences:
Path: C:\Users\wy\AppData\Roaming\MathWorks\MATLAB\cvx_prefs.mat
License host:
Username: wy
Host ID: b4b52fdabe98 (eth3)
Installed license:
Also in file: C:\Users\wy\Downloads\cvx_license.dat
Organization: southeast university
Contact: meng hua (mhua@seu.edu.cn)
License type: academic
Named user: wy
Host ID: b4b52fdabe98
Expiration: 2019-04-25 (175 days remaining)
Status: verified
---------------------------------------------------------------------------
How to verify that the CVXQUAD is correctly installed in my matlab ?
I recommend removing all CVX and CVXQUAD directories from your MATLAB path, then reinstall CVX and install CVXQUAD and its exponential.m replacement. Then try running a CVXQUAD example. Perhaps something got corrupted in your installation.
Dear Mark,
I try various ways to install CVXQUAD, even reinstall the CVXQUAD in another computer, but still failed. When I use the following code .
n = 4;
M = randn(n,n);
M = M*M';
cvx_begin
variable X(n,n) symmetric
minimize quantum_rel_entr(M,X)
subject to
diag(X) == ones(n,1)
cvx_end
The matlab window shows:
Error using evalin
undefined function âquantum_rel_entrâ for input arguments of type âcvxâ .
Error minimize (line 8)
x = evalin( âcallerâ, sprintf( '%s ', varargin{:} ) );
Error test (line 6)
minimize quantum_rel_entr(M,X)
I donnot know why I cannot install it correctly .
Did you remember to include the folder containing CVXQUAD in your MATLAB path?
If the folder containing CVVXQUAD is in your MATLAB path, then have suggested everything I can. You can try opening an issue at https://github.com/hfawzi/cvxquad/issues . You should include the output from cvx_version when you submit the issue.
So far, you are the only poster I know of who tried to install CVXQUAD and did not succeed.
Dear mark,
I am sure the folder is added in my MATLA path as you see the previous attached figure. I download the folder, extract it and copy it in the cvx file, then copy the experimental file to âsetsâ file.
Have you explicitly checked that the cvxquad-mater folder is in the MATLAB path? Donât assume that it is. I doubt it was added by CVX to your MATLAB path, despite being under a CVX directory. So if you havenât added it to your path, it won;t be in it.
Dear mark,
Thanks for your kind explanations. I think i know where is wrong. thank you very much!
Please let us know what happens when you use CVXQUAD on this problem (with Mosek and.or whatever other solvers you try).
Dear Mark,
The CVXQUAD works now. Thanks for your help.
And was the problem you posted in this thread successfully solved using CVXQUAD? Can you show us the CVX and solver output?
Dear Mark,
The folder of CVXQUAD was put in wrong path before., and I corret it and works now.
The output of solver is given as following:
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================
Calling SeDuMi 1.34: 38876 variables, 14740 equality constraints
For improved efficiency, SeDuMi is solving the dual problem.
------------------------------------------------------------
SeDuMi 1.34 (beta) 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 = 14740, order n = 27357, dim = 38877, blocks = 11521
nnz(A) = 58240 + 0, nnz(ADA) = 56160, nnz(L) = 36156
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 9.00E+03 0.000
1 : 1.74E+04 6.27E+03 0.000 0.6974 0.9000 0.9000 2.69 1 1 3.5E+01
2 : 5.93E+03 3.65E+03 0.000 0.5817 0.9000 0.9000 4.39 1 1 7.4E+00
3 : 2.25E+03 1.92E+03 0.000 0.5251 0.9000 0.9000 2.43 1 1 2.7E+00
4 : 5.53E+02 8.06E+02 0.000 0.4205 0.9000 0.9000 1.72 1 1 9.6E-01
5 : -2.27E+02 4.38E+02 0.000 0.5439 0.9000 0.9000 1.28 1 1 5.7E-01
6 : -7.26E+02 2.50E+02 0.000 0.5714 0.9000 0.9000 1.04 1 1 4.1E-01
7 : -7.26E+02 2.44E+01 0.000 0.0976 0.9000 0.0000 1.00 1 1 2.0E-01
8 : -1.24E+03 2.77E-06 0.000 0.0000 0.8876 0.9000 0.95 1 1 5.0E-02
9 : -1.42E+03 1.30E-06 0.000 0.4690 0.9099 0.9000 0.78 1 1 2.7E-02
10 : -1.49E+03 9.27E-07 0.000 0.7122 0.9000 0.9000 0.70 1 1 2.1E-02
11 : -1.55E+03 7.10E-07 0.000 0.7661 0.9000 0.7991 0.44 1 1 1.8E-02
12 : -1.60E+03 5.23E-07 0.000 0.7373 0.9000 0.9000 0.35 1 1 1.5E-02
13 : -1.60E+03 2.80E-07 0.000 0.5353 0.9000 0.0000 0.42 1 1 1.1E-02
14 : -1.73E+03 1.07E-07 0.000 0.3833 0.9100 0.9000 0.26 1 1 4.8E-03
15 : -1.83E+03 5.29E-08 0.000 0.4930 0.9000 0.9265 0.10 4 5 3.5E-03
16 : -1.88E+03 2.75E-08 0.000 0.5203 0.9000 0.7006 0.17 4 5 2.7E-03
17 : -1.95E+03 1.24E-08 0.000 0.4496 0.9000 0.9000 0.23 1 4 1.7E-03
18 : -1.99E+03 6.51E-09 0.000 0.5258 0.9000 0.9000 0.29 1 4 1.2E-03
19 : -2.03E+03 3.90E-09 0.000 0.5995 0.9000 0.9000 0.25 2 4 9.0E-04
20 : -2.07E+03 2.18E-09 0.000 0.5590 0.9000 0.9000 0.25 2 8 6.6E-04
21 : -2.11E+03 1.26E-09 0.000 0.5781 0.9000 0.9000 0.25 2 9 4.9E-04
22 : -2.14E+03 8.09E-10 0.000 0.6415 0.9000 0.9000 0.22 2 8 4.0E-04
23 : -2.16E+03 5.32E-10 0.000 0.6575 0.9000 0.9000 0.19 2 10 3.2E-04
24 : -2.19E+03 3.32E-10 0.000 0.6239 0.9000 0.9000 0.20 2 13 2.5E-04
25 : -2.22E+03 2.17E-10 0.000 0.6538 0.9000 0.9000 0.21 2 13 2.0E-04
26 : -2.24E+03 1.51E-10 0.000 0.6940 0.9000 0.9000 0.19 2 7 1.7E-04
27 : -2.27E+03 1.05E-10 0.000 0.6967 0.9000 0.9000 0.18 2 7 1.4E-04
28 : -2.29E+03 7.05E-11 0.000 0.6713 0.9000 0.9000 0.19 2 7 1.2E-04
29 : -2.31E+03 4.93E-11 0.000 0.6992 0.9000 0.9000 0.20 2 7 9.7E-05
30 : -2.33E+03 3.58E-11 0.000 0.7258 0.9000 0.9000 0.18 1 15 8.3E-05
31 : -2.35E+03 2.58E-11 0.000 0.7210 0.9000 0.9000 0.18 1 15 7.1E-05
32 : -2.37E+03 1.82E-11 0.000 0.7058 0.9000 0.9000 0.19 1 14 5.9E-05
33 : -2.39E+03 1.32E-11 0.000 0.7276 0.9000 0.9000 0.19 1 14 5.0E-05
34 : -2.41E+03 9.85E-12 0.000 0.7440 0.9000 0.9000 0.18 1 25 4.4E-05
35 : -2.43E+03 7.29E-12 0.000 0.7402 0.9000 0.9000 0.18 1 17 3.8E-05
36 : -2.45E+03 5.28E-12 0.000 0.7237 0.9000 0.9000 0.18 1 16 3.2E-05
37 : -2.47E+03 3.82E-12 0.000 0.7247 0.9000 0.9000 0.17 1 16 2.7E-05
38 : -2.49E+03 2.80E-12 0.000 0.7322 0.9000 0.9000 0.18 1 19 2.3E-05
39 : -2.51E+03 2.06E-12 0.000 0.7339 0.9000 0.9000 0.13 1 18 2.0E-05
40 : -2.53E+03 1.46E-12 0.000 0.7121 0.9000 0.9000 0.14 1 18 1.7E-05
41 : -2.55E+03 1.04E-12 0.000 0.7080 0.9000 0.9000 0.11 1 17 1.4E-05
42 : -2.57E+03 7.30E-13 0.000 0.7048 0.9000 0.9000 0.10 1 19 1.2E-05
43 : -2.60E+03 4.90E-13 0.000 0.6709 0.9000 0.9000 0.08 1 19 9.8E-06
44 : -2.62E+03 3.21E-13 0.000 0.6546 0.9000 0.9000 0.09 1 19 7.9E-06
45 : -2.65E+03 2.02E-13 0.000 0.6301 0.9000 0.9000 0.09 1 18 6.3E-06
46 : -2.68E+03 1.32E-13 0.000 0.6528 0.9000 0.9000 0.09 1 33 5.1E-06
47 : -2.70E+03 8.35E-14 0.000 0.6331 0.9000 0.9000 0.08 1 20 4.0E-06
48 : -2.73E+03 5.48E-14 0.000 0.6563 0.9000 0.9000 0.08 1 22 3.3E-06
49 : -2.75E+03 3.94E-14 0.000 0.7190 0.9000 0.9000 0.07 1 19 2.8E-06
50 : -2.77E+03 2.95E-14 0.000 0.7482 0.9000 0.9000 0.05 1 19 2.4E-06
51 : -2.79E+03 2.02E-14 0.000 0.6843 0.9000 0.9000 0.04 1 23 2.0E-06
52 : -2.81E+03 1.41E-14 0.000 0.6976 0.9000 0.9000 0.03 1 27 1.7E-06
53 : -2.82E+03 1.08E-14 0.000 0.7643 0.9000 0.9000 0.04 1 22 1.5E-06
54 : -2.84E+03 8.65E-15 0.000 0.8037 0.9000 0.9000 0.03 3 33 1.3E-06
55 : -2.86E+03 6.39E-15 0.000 0.7385 0.9000 0.9000 0.03 1 37 1.1E-06
56 : -2.87E+03 4.73E-15 0.000 0.7408 0.9000 0.9000 0.03 1 21 9.6E-07
57 : -2.89E+03 3.75E-15 0.000 0.7928 0.9000 0.9000 0.04 3 25 8.6E-07
58 : -2.90E+03 3.10E-15 0.000 0.8258 0.9000 0.9000 0.04 1 32 7.8E-07
59 : -2.91E+03 2.46E-15 0.000 0.7932 0.9000 0.9000 0.04 3 29 6.9E-07
60 : -2.93E+03 1.91E-15 0.072 0.7767 0.9000 0.9000 0.04 3 21 6.1E-07
61 : -2.94E+03 1.55E-15 0.208 0.8125 0.9000 0.9000 0.04 3 24 5.5E-07
62 : -2.95E+03 1.33E-15 0.151 0.8586 0.9000 0.9000 0.04 3 30 5.1E-07
63 : -2.96E+03 1.16E-15 0.098 0.8699 0.9000 0.9000 0.03 3 39 4.7E-07
64 : -2.97E+03 7.66E-16 0.001 0.6615 0.9282 0.9000 0.03 3 27 3.8E-07
65 : -2.99E+03 6.37E-16 0.347 0.8310 0.9000 0.9196 0.03 23 30 3.5E-07
66 : -2.99E+03 5.63E-16 0.341 0.8844 0.9000 0.9022 0.06 3 32 3.2E-07
67 : -3.00E+03 5.05E-16 0.401 0.8970 0.9000 0.9273 0.06 3 29 3.1E-07
68 : -3.01E+03 4.47E-16 0.391 0.8850 0.9000 0.9084 0.07 3 49 2.9E-07
69 : -3.02E+03 3.84E-16 0.255 0.8598 0.9000 0.9002 0.07 3 32 2.7E-07
70 : -3.03E+03 3.22E-16 0.163 0.8369 0.9037 0.9000 0.06 3 25 2.4E-07
71 : -3.04E+03 2.64E-16 0.117 0.8206 0.9063 0.9000 0.04 3 34 2.2E-07
72 : -3.05E+03 2.17E-16 0.125 0.8210 0.9000 0.9016 0.02 5 42 2.0E-07
Run into numerical problems.
iter seconds digits c*x b*y
72 21.5 Inf -3.0523682468e+03 -3.0513505341e+03
|Ax-b| = 9.7e-06, [Ay-c]_+ = 2.3E-07, |x|= 5.3e+07, |y|= 5.5e+07
Detailed timing (sec)
Pre IPM Post
6.710E-01 1.170E+01 6.599E-02
Max-norms: ||b||=1.154156e+01, ||c|| = 4.058503e+01,
Cholesky |add|=1771, |skip| = 0, ||L.L|| = 215.832.
------------------------------------------------------------
Status: Inaccurate/Solved
Optimal value (cvx_optval): +1533.79Hmm, that;s not too great because SeDuMi ran into numerical problems and CVX declared it inaccurate/solved.
Can you try it with Mosek and SDPT3, and if you have it, Gurobi?
Dear Mark,
I try to run the code with Mosek and SDPT3. Unfortunately, The MOSEK fails, and the matlab is crashed when use SDPT3.
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================
=====================================
Using Pade approximation for exponential
cone with parameters m=3, k=3
=====================================
Calling Mosek 8.0.0.60: 38876 variables, 14740 equality constraints
For improved efficiency, Mosek is solving the dual problem.
------------------------------------------------------------
MOSEK Version 8.0.0.60 (Build date: 2017-3-1 13:09:33)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
MOSEK warning 710: #3 (nearly) zero elements are specified in sparse col '' (2) of matrix 'A'.
MOSEK warning 710: #4 (nearly) zero elements are specified in sparse col '' (3) of matrix 'A'.
MOSEK warning 710: #3 (nearly) zero elements are specified in sparse col '' (7) of matrix 'A'.
MOSEK warning 710: #4 (nearly) zero elements are specified in sparse col '' (8) of matrix 'A'.
MOSEK warning 710: #3 (nearly) zero elements are specified in sparse col '' (12) of matrix 'A'.
MOSEK warning 710: #4 (nearly) zero elements are specified in sparse col '' (13) of matrix 'A'.
MOSEK warning 710: #3 (nearly) zero elements are specified in sparse col '' (17) of matrix 'A'.
MOSEK warning 710: #4 (nearly) zero elements are specified in sparse col '' (18) of matrix 'A'.
MOSEK warning 710: #3 (nearly) zero elements are specified in sparse col '' (22) of matrix 'A'.
MOSEK warning 710: #5 (nearly) zero elements are specified in sparse col '' (23) of matrix 'A'.
Warning number 710 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 14740
Cones : 11520
Scalar variables : 38876
Matrix variables : 0
Integer variables : 0
Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 292
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.05
Optimizer - threads : 2
Optimizer - solved problem : the primal
Optimizer - Constraints : 6856
Optimizer - Cones : 11520
Optimizer - Scalar variables : 36183 conic : 34560
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.05 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 2.07e+004 after factor : 2.12e+004
Factor - dense dim. : 0 flops : 2.95e+005
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 4.3e+000 1.0e+001 2.2e+003 0.00e+000 3.775560871e+004 2.456078795e+003 1.0e+000 0.20
1 2.9e+000 6.9e+000 2.3e+003 7.82e-002 1.863605495e+004 -2.868629310e+003 6.8e-001 0.33
2 1.7e+000 3.9e+000 1.8e+003 4.70e-001 1.118263278e+004 -1.404844579e+003 3.8e-001 0.36
3 3.6e-001 8.5e-001 1.0e+003 9.02e-001 2.166740272e+003 -4.727152052e+002 8.4e-002 0.38
4 1.5e-001 3.5e-001 5.8e+002 1.19e+000 -1.570638054e+001 -1.061732219e+003 3.5e-002 0.41
5 8.3e-002 2.0e-001 4.1e+002 1.07e+000 -7.343220648e+002 -1.313588258e+003 1.9e-002 0.44
6 3.3e-002 7.7e-002 2.3e+002 9.99e-001 -1.305856724e+003 -1.543421271e+003 7.6e-003 0.45
7 2.4e-002 5.6e-002 1.8e+002 8.04e-001 -1.420242709e+003 -1.612174240e+003 5.5e-003 0.48
8 1.0e-002 2.5e-002 1.1e+002 8.41e-001 -1.649675132e+003 -1.741374948e+003 2.4e-003 0.50
9 8.3e-003 2.0e-002 8.5e+001 5.80e-001 -1.685959474e+003 -1.769475857e+003 1.9e-003 0.53
10 3.3e-003 7.8e-003 4.3e+001 6.16e-001 -1.833239951e+003 -1.875052764e+003 7.7e-004 0.56
11 1.5e-003 3.5e-003 2.3e+001 5.68e-001 -1.923036343e+003 -1.946950632e+003 3.5e-004 0.58
12 1.1e-003 2.5e-003 1.5e+001 2.29e-001 -1.947055160e+003 -1.970097919e+003 2.5e-004 0.61
13 3.2e-004 7.5e-004 5.6e+000 3.98e-001 -2.061654911e+003 -2.071236846e+003 7.4e-005 0.64
14 1.2e-004 2.9e-004 2.1e+000 2.77e-001 -2.129926079e+003 -2.136061607e+003 2.9e-005 0.66
15 5.7e-005 1.3e-004 1.0e+000 3.04e-001 -2.187382812e+003 -2.191297036e+003 1.3e-005 0.69
16 1.9e-005 4.5e-005 3.7e-001 2.72e-001 -2.260566339e+003 -2.262696012e+003 4.4e-006 0.72
17 8.5e-006 2.0e-005 1.6e-001 1.96e-001 -2.311063134e+003 -2.312561753e+003 2.0e-006 0.73
18 2.7e-006 6.3e-006 5.3e-002 2.20e-001 -2.386604705e+003 -2.387363897e+003 6.2e-007 0.77
19 1.2e-006 2.8e-006 2.2e-002 1.28e-001 -2.433711070e+003 -2.434283367e+003 2.8e-007 0.78
20 4.9e-007 1.1e-006 1.0e-002 3.21e-001 -2.495232078e+003 -2.495545899e+003 1.1e-007 0.81
21 2.9e-007 6.7e-007 5.2e-003 1.97e-002 -2.521843926e+003 -2.522135393e+003 6.6e-008 0.84
22 7.7e-008 1.8e-007 1.7e-003 2.32e-001 -2.609318412e+003 -2.609434770e+003 1.8e-008 0.86
23 2.9e-008 6.7e-008 5.5e-004 7.35e-002 -2.664982811e+003 -2.665058293e+003 6.6e-009 0.89
24 9.1e-009 2.1e-008 2.0e-004 2.21e-001 -2.736005920e+003 -2.736040005e+003 2.1e-009 0.91
25 4.0e-009 9.5e-009 7.4e-005 -2.25e-003 -2.780206594e+003 -2.780228756e+003 9.4e-010 0.94
26 1.1e-009 2.7e-009 2.4e-005 2.16e-001 -2.860221405e+003 -2.860227421e+003 2.7e-010 0.97
27 4.6e-010 2.2e-009 8.8e-006 1.21e-001 -2.912393893e+003 -2.912393421e+003 1.1e-010 0.98
28 1.5e-010 1.0e-008 3.2e-006 2.38e-001 -2.979096095e+003 -2.979092527e+003 3.5e-011 1.01
29 7.3e-011 1.4e-008 1.4e-006 6.09e-002 -3.017852197e+003 -3.017844859e+003 1.7e-011 1.03
30 2.1e-011 5.8e-008 4.5e-007 2.30e-001 -3.094184842e+003 -3.094178052e+003 4.8e-012 1.06
31 7.7e-012 1.2e-007 1.5e-007 6.89e-002 -3.147460059e+003 -3.147450047e+003 1.8e-012 1.09
32 2.7e-012 6.3e-007 6.1e-008 3.04e-001 -3.210689717e+003 -3.210682272e+003 6.3e-013 1.11
33 1.3e-012 8.4e-007 2.5e-008 2.89e-002 -3.246810778e+003 -3.246800542e+003 3.0e-013 1.14
34 3.5e-013 3.8e-006 7.9e-009 1.64e-001 -3.321231081e+003 -3.321222837e+003 8.2e-014 1.16
35 1.3e-013 2.6e-005 2.6e-009 4.84e-002 -3.372776623e+003 -3.372766206e+003 3.0e-014 1.19
36 5.3e-013 1.3e-004 2.5e-009 2.56e-001 -3.375000547e+003 -3.374990223e+003 2.9e-014 1.29
37 5.3e-013 1.3e-004 2.5e-009 2.50e-001 -3.375044814e+003 -3.375034491e+003 2.9e-014 1.37
38 5.1e-013 1.3e-004 2.4e-009 2.49e-001 -3.377606712e+003 -3.377596493e+003 2.8e-014 1.48
39 5.0e-013 1.3e-004 2.4e-009 2.44e-001 -3.378169633e+003 -3.378159436e+003 2.8e-014 1.59
40 5.0e-013 1.3e-004 2.4e-009 2.42e-001 -3.378242396e+003 -3.378232202e+003 2.7e-014 1.69
41 4.6e-013 1.2e-004 2.2e-009 2.41e-001 -3.383506040e+003 -3.383496050e+003 2.5e-014 1.78
42 4.6e-013 1.2e-004 2.2e-009 2.31e-001 -3.383602825e+003 -3.383592838e+003 2.5e-014 1.90
43 5.7e-013 1.2e-004 2.2e-009 2.30e-001 -3.384186740e+003 -3.384176775e+003 2.5e-014 2.01
44 5.6e-013 1.2e-004 2.2e-009 2.30e-001 -3.384746768e+003 -3.384736823e+003 2.5e-014 2.11
45 5.5e-013 1.1e-004 2.1e-009 2.28e-001 -3.385523675e+003 -3.385513758e+003 2.4e-014 2.21
46 5.7e-013 1.1e-004 2.1e-009 2.26e-001 -3.385999927e+003 -3.385990027e+003 2.4e-014 2.31
47 5.4e-013 1.1e-004 2.0e-009 2.25e-001 -3.388601509e+003 -3.388591701e+003 2.3e-014 2.40
48 5.4e-013 1.1e-004 2.0e-009 2.20e-001 -3.388868824e+003 -3.388859025e+003 2.3e-014 2.51
49 4.9e-013 9.8e-005 1.9e-009 2.19e-001 -3.394188156e+003 -3.394178537e+003 2.1e-014 2.61
50 5.1e-013 9.6e-005 1.8e-009 2.10e-001 -3.395397982e+003 -3.395388402e+003 2.1e-014 2.75
51 4.8e-013 9.6e-005 1.8e-009 2.08e-001 -3.395673489e+003 -3.395663918e+003 2.1e-014 2.84
52 4.1e-013 8.1e-005 1.6e-009 2.07e-001 -3.405755794e+003 -3.405746540e+003 1.7e-014 2.92
53 4.5e-013 8.0e-005 1.6e-009 1.96e-001 -3.406340880e+003 -3.406331642e+003 1.7e-014 3.01
54 4.5e-013 8.0e-005 1.6e-009 1.95e-001 -3.406451531e+003 -3.406442296e+003 1.7e-014 3.09
55 4.5e-013 9.8e-005 1.4e-009 1.94e-001 -3.411138027e+003 -3.411128925e+003 1.6e-014 3.18
56 4.3e-013 1.1e-004 1.4e-009 1.88e-001 -3.412916674e+003 -3.412907620e+003 1.5e-014 3.28
57 4.3e-013 1.1e-004 1.4e-009 1.86e-001 -3.413447609e+003 -3.413438570e+003 1.5e-014 3.38
58 4.3e-013 1.0e-004 1.4e-009 1.85e-001 -3.413527456e+003 -3.413518418e+003 1.5e-014 3.50
59 4.1e-013 1.0e-004 1.3e-009 1.85e-001 -3.416133256e+003 -3.416124287e+003 1.4e-014 3.57
60 4.1e-013 9.9e-005 1.3e-009 1.82e-001 -3.416604825e+003 -3.416595868e+003 1.4e-014 3.67
61 3.7e-013 9.5e-005 1.2e-009 1.81e-001 -3.421946019e+003 -3.421937200e+003 1.3e-014 3.77
62 3.7e-013 9.5e-005 1.2e-009 1.76e-001 -3.422058822e+003 -3.422050005e+003 1.3e-014 3.87
63 2.2e-013 1.7e-004 4.4e-010 1.75e-001 -3.481107941e+003 -3.481100586e+003 4.3e-015 3.96
64 2.2e-013 1.7e-004 4.4e-010 1.26e-001 -3.481107941e+003 -3.481100586e+003 4.3e-015 4.06
Interior-point optimizer terminated. Time: 4.20.
Optimizer terminated. Time: 4.27
Interior-point solution summary
Problem status : ILL_POSED
Solution status : DUAL_ILLPOSED_CER
Primal. obj: -1.5179485844e-002 nrm: 6e+002 Viol. con: 4e-012 var: 2e-006 cones: 3e-005
Optimizer summary
Optimizer - time: 4.27
Interior-point - iterations : 65 time: 4.20
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
Mosek error: MSK_RES_TRM_STALL ()
------------------------------------------------------------
Status: Failed
Optimal value (cvx_optval): NaNLook at A. Mosek is warning about small non-zero elements. What is the magnitude of the smallest magnitude non-zero element in A ? Either re-scaling is needed, or perhaps roundoff error level non-zero elements in A should be set to exactly zero.
Mosek was not able to achieve termination criteria, :appearing to âblameâ it on the problem being dual ill-posed Given that CVX passed the dual of your original problem to Mosek, I think this means that Mosek has found your primal problem to be ill-posed. Perhaps very small magnitude non-zero elements in A are contributing to or causing this ill-posedness.
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Now 3 optimizers could not produce an optimal solution.
And Mosek tells you that your problem is broken. SeDuMi says
|Ax-b| = 9.7e-06, [Ay-c]_+ = 2.3E-07, |x|= 5.3e+07, |y|= 5.5e+07
so that indicates attainment issues since the solutions are very large,
So maybe the conclusion is that your problem is badly posed.
Dear Mark,
I will try and rescale some parameter vaules, then run the code.
Dear Erling,
I agree with you, and I will have a try through rescaling some parameter values.
@Rachel_hua Please read and carefully study my new CVXQUAD META post (you inspired me to include one particular sentence in the installation instructions 
). CVXQUAD: How to use CVXQUADâs Pade Approximant instead of CVXâs unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUADâs Quantum (Matrix) Entropy & Matrix Log related functions This may help you and others for future proiblems, and hopefully reduce my posting burdens, as Iâd like to slide into semi-retirement as a question answerer on this forum.
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Thank you Mark, I will read your CVXQUAD META post.
It is no longer META, but it is pinned.
I hope everyone who uses the relevant functions or modes will read it. And for those who donât, my answer may just consist of linking to it unoless there is something new in their post which isnât covered (yet) in the pinned thread.