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