randn('state', 0);
rand('state', 0);
n = 20;
m = 10;
p = 5;
tmp = rand(n,1);
A = randn(m,n);
b = A*tmp;
F = randn(p,n);
g = F*tmp + rand(p,1);
cvx_begin
variable x(n)
maximize sum(entr(x))
A*x == b
F*x <= g
cvx_end
display('The optimal solution is:' );
disp(x);
Calling Mosek 9.1.9: 65 variables, 35 equality constraints
------------------------------------------------------------
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:32:15)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: MACOSX/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 35
Cones : 20
Scalar variables : 65
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 35
Cones : 20
Scalar variables : 65
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 15
Optimizer - Cones : 20
Optimizer - Scalar variables : 65 conic : 60
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 120 after factor : 120
Factor - dense dim. : 0 flops : 1.08e+04
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.1e+00 8.1e-01 4.3e+01 0.00e+00 1.655676798e+01 -2.581855420e+01 1.0e+00 0.00
1 1.4e-01 9.9e-02 1.3e+00 1.02e+00 -3.813483321e+00 -8.739805594e+00 1.2e-01 0.01
2 1.6e-02 1.2e-02 5.3e-02 1.06e+00 -5.496053237e+00 -6.066607212e+00 1.5e-02 0.01
3 4.8e-04 3.4e-04 2.6e-04 1.01e+00 -5.697190435e+00 -5.713659083e+00 4.3e-04 0.01
4 2.5e-05 1.8e-05 3.2e-06 1.00e+00 -5.703012589e+00 -5.703882057e+00 2.2e-05 0.01
5 2.6e-06 1.9e-06 1.0e-07 1.00e+00 -5.703310903e+00 -5.703399767e+00 2.3e-06 0.01
6 1.8e-07 1.3e-07 2.0e-09 1.00e+00 -5.703342595e+00 -5.703348873e+00 1.6e-07 0.01
7 1.8e-08 1.3e-08 6.3e-11 1.00e+00 -5.703344777e+00 -5.703345393e+00 1.6e-08 0.01
8 8.8e-09 1.8e-09 3.2e-12 1.00e+00 -5.703344991e+00 -5.703345076e+00 2.3e-09 0.01
Optimizer terminated. Time: 0.01
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -5.7033449908e+00 nrm: 7e+00 Viol. con: 2e-08 var: 3e-09 cones: 3e-09
Dual. obj: -5.7033450757e+00 nrm: 1e+00 Viol. con: 0e+00 var: 3e-24 cones: 0e+00
Optimizer summary
Optimizer - time: 0.01
Interior-point - iterations : 8 time: 0.01
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: Solved
Optimal value (cvx_optval): +5.70334
The optimal solution is:
0.3445
0.3181
0.7539
0.8020
0.6418
0.3517
0.1981
0.2578
0.6373
0.3357
0.7109
0.8998
0.6085
0.6444
0.3061
0.4522
0.8886
0.7801
0.3106
0.6131