# Inconsistent results

I have encounter the following unreasonable behavior of CVX for a feasibility problem. The code given in the sequel yields “status: solved”. When the line “x(2:4)==0;” is commented, thereby removing a constraint, extending the optimization space and making the problem less restrictive, I get “status: infeasible”.

I would appreciate any help on that topic.
the code:

c11 = 275.1; c22 = 275.1;
c33 = 164.9; m23 = 54; m13 = 54.3; m12 = 113.1;
c12 = 179; c13 = 151.6; c23 = 151.6;
cvx_begin sdp
variable m;
variable x(12);
expression DMTl4(3,3);
DMTl4 = [4 .* m13 + (-1) .* x(2) + (-2) .* x(5) + (-1) .* x(8) + (-2) .* …
x(10),4 .* m13 + (-2) .* x(5) + (-1 / 2) .* x(8),4 .* m13 + (-2) .* …
x(5) + (-1) .* x(8) + (-1) .* x(12);4 .* m13 + (-2) .* x(5) + (-1 …

/ 2) .* x(8),4 .* m13 + (-2) .* (x(5) + x(10)),4 .* m13 + (-2) .* …
x(5) + (-1 / 2) .* x(8);4 .* m13 + (-2) .* x(5) + (-1) .* x(8) + (-1) …
.* x(12),4 .* m13 + (-2) .* x(5) + (-1 / 2) .* x(8),4 .* m13 + ( …

-1) .* x(2) + (-2) .* x(5) + (-1) .* x(8) + (-2) .* x(10)];
x(10)==0;
x(11)==0;
x(12)==0;
x(2:4)==0; %when this line is commented , the output of Infeasible
4 .* m + (-2) .* x(5) + (-2) .* x(10)>=0;
DMTl4>=0;
m>=0;
cvx_end

Which version of CVX are you using? Which solver is doing this? Have you tried the other solvers; if not, please do so; and if so, do they give the same result?

CVX version 2.1. This phenomenon occurs with SeDuMi and Mosek 7.1. SDPT3 solves both cases, with different results. You suggest then that the problem is the solver?

No, based on your feedback, I am not inclined to blame a solver per se. It is possible, however, that we’re dealing with a near-infeasible problem, in which case all sorts of weird things can happen, some of which are solver-dependent.