CVX Ill_posed: SOCP

1

Hello everyone,
I met a problem in solving SOCP with CVX based on MOSEK 10.2.
I think the constraints are all convex, but the output information is
[Problem status : ILL_POSED
Solution status : DUAL_ILLPOSED_CER]
How can I solve this problem?

I use majorization-minimization algorithm (corresponding to the while loop in my code), similar to successive convex approximation. But the output information below is shown in the first while loop, and the program execution stops.

The following are my code and complete output information of CVX and MOSEK

2

V=10;U=10;
R=rand(V,U);
temp=rand(V,U);
indicator=temp>0.5;
R=R.indicator1e0;

comp_ub=4*ones(V,1);
task_strength=rand(U,1)*400;
task_strength_mat=repmat(task_strength.‘,V,1);
task_cycle=rand(U,1)*1e3;
task_cycle_mat=repmat(task_cycle.’,V,1);

task_off_init=rand(V,U).*indicator;
temp=sum(task_off_init,1);
temp=repmat(temp,V,1);
task_off_sqrt=sqrt(task_off_init./temp);

task_off_sqrt_rec=0;

task_off_diff=sum(sum((task_off_sqrt_rec-task_off_sqrt).^2))/V/U;

eps=1e-4;
while(task_off_diff>=1e-4)

task_off_sqrt_rec=task_off_sqrt;
cvx_solver mosek_6
cvx_begin 
    variable task_off(V,U)
    variable comp_allo(V,U)
    variable task_off_sqrt(V,U)
    variable time_min_opt
    variable rho_1(V,U)
    variable rho_2(V,U)

    minimize(time_min_opt)
    subject to
        comp_allo>=0;
        sum(comp_allo,2)<=comp_ub;
        task_off_sqrt>=-ones(V,U);
        task_off_sqrt<=ones(V,U);
        sum(task_off_sqrt.^2,1)<=ones(1,U);
        sum(2*task_off_sqrt_rec.*task_off_sqrt-task_off_sqrt_rec.^2,1)>=ones(1,U);
        rho_1>=0;
        rho_2>=0;
        rho_1+rho_2<=time_min_opt*ones(V,U);
        task_strength_mat.*(task_off_sqrt.^2)-rho_1.*R<=0;
        for loop_v=1:V
            for loop_u=1:U
                norm([comp_allo(loop_v,loop_u)-rho_2(loop_v,loop_u);sqrt(4*task_strength_mat(loop_v,loop_u)*task_cycle_mat(loop_v,loop_u))*task_off_sqrt(loop_v,loop_u)])<=comp_allo(loop_v,loop_u)+rho_2(loop_v,loop_u);
            end
        end
cvx_end
task_off_diff=sum(sum((task_off_sqrt_rec-task_off_sqrt).^2))/V/U;

end

3

Calling Mosek_6 10.1.12: 1730 variables, 701 equality constraints
For improved efficiency, Mosek_6 is solving the dual problem.

MOSEK Version 10.2.6 (Build date: 2024-10-16 08:25:10)
Copyright (c) MOSEK ApS, Denmark WWW: mosek.com
Platform: Windows/64-X86

Problem
Name :
Objective sense : minimize
Type : CONIC (conic optimization problem)
Constraints : 701
Affine conic cons. : 0
Disjunctive cons. : 0
Cones : 300
Scalar variables : 1730
Matrix variables : 0
Integer variables : 0

Optimizer started.
Presolve started.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 0 time : 0.00
Lin. dep. - primal attempts : 0 successes : 0
Lin. dep. - dual attempts : 0 successes : 0
Lin. dep. - primal deps. : 0 dual deps. : 0
Presolve terminated. Time: 0.00
Optimizer terminated. Time: 0.00

Interior-point solution summary
Problem status : ILL_POSED
Solution status : DUAL_ILLPOSED_CER
Primal. obj: 0.0000000000e+00 nrm: 1e+00 Viol. con: 0e+00 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.00
Interior-point - iterations : 0 time: 0.00
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

4

Mosek reported it is dual ill-posed, and Mosek was provided the dual by CVX. So the problem is assessed by Mosek to be primal ill-posed. I will defer to Mosek personnel for any assessment.

5

Thanks for your help, Mark.
When I have run into problems with CVX in the past, it has always been helpful to find your helpful responses to similar issues in this forum. When people I know have problems with CVX, I always say to them: Go look up what Mark says, it helps.
Thank you very much for your selfless contribution. :clap:

6

Your problem is very close to being primal infeasible.

For instance the problem

min 0
st. 1/x <= 0
x >= 0

is primal ill-posed.

You can expect things like this unless you have proof that successive convex programing is working.

7

Thank you for your help. Many thanks. :+1: