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