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
0.5*x(l)

*log(p1) - 0.5*log(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