I am solving a convex problem in CVX 2.2 with Mosek 9.1.9. But every time it fails.
The following is the output. Could you please tell me what is wrong here. I think this problem abides by the DCP ruleset.
cvx_begin
cvx_precision default
cvx_solver mosek
variables obj(1) rho(n*m,1) p_ub(K,1) x(K,1)
minimize (obj)
rho’c + sqrt(p0/(1-p0))norm(COV_crho,2) <= obj;
for l = 1:K
0.5x(l)log(p1) - 0.5log(1-p_ub(l)) + log(V(l)) <= log(xi(l) - rho’*d{l});
x(l)*log(p1) <= log(p_ub(l));
end
sum(x) == 1;
x >= 0;
rho’*A == (1-alpha)*gamma’;
rho >= 0;
cvx_end
CVX Warning:
Models involving “log” 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: 1152 variables, 531 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 (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 531
Cones : 31
Scalar variables : 1152
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 1
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 : 531
Cones : 31
Scalar variables : 1152
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 12
Optimizer - solved problem : the primal
Optimizer - Constraints : 529
Optimizer - Cones : 32
Optimizer - Scalar variables : 1152 conic : 642
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 : 2.17e+04 after factor : 2.46e+04
Factor - dense dim. : 83 flops : 1.44e+06
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.5e+01 4.9e+01 6.2e+02 0.00e+00 6.130126956e+02 -3.000000000e+00 1.0e+00 0.00
1 1.5e+01 4.9e+01 6.2e+02 -5.93e+00 6.130126956e+02 -3.000000000e+00 1.0e+00 0.00
2 1.5e+01 4.9e+01 6.2e+02 -5.93e+00 6.130126956e+02 -3.000000000e+00 1.0e+00 0.02
Optimizer terminated. Time: 0.02
Interior-point solution summary
Problem status : UNKNOWN
Solution status : UNKNOWN
Primal. obj: 6.1301269559e+02 nrm: 2e+03 Viol. con: 7e+03 var: 0e+00 cones: 0e+00
Dual. obj: -3.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 5e+01 cones: 0e+00
Optimizer summary
Optimizer - time: 0.02
Interior-point - iterations : 3 time: 0.02
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
