After adding new constraints, cvx_status is 'Infeasible'

The cvx_status obtained by the original optimization problem is ‘solved’, but when a new constraint (2) is added, the obtained cvx_status is ‘Infeasible’。The newly added constraint is also convex, but why does it make the problem ‘Infeasible’? Hope someone can help me out. thank you very much!

Among them, v and W are the matrix with given value, the value of noise and t have been given, and Q , Betaa and z are the variables to be optimized.

The original optimization problem:
cvx_solver mosek
cvx_save_prefs
cvx_begin quiet
variable Q(N+1,N+1) hermitian
variables Betaa(1)
variable z(1)
constraint(1) = trace(QvW*v’)+noise-z;
maximize 1/t(log(1+Betaa)/log(2)
subject to
real(constraint)<=0;
Q == hermitian_semidefinite(N+1);
diag(Q) ==1;
cvx_end
At this time, cvx_status: ‘solved’.

Optimization problem after adding new constraints:
cvx_solver mosek
cvx_save_prefs
cvx_begin quiet
variable Q(N+1,N+1) hermitian
variables Betaa(1)
variable z(1)
constraint(1) = trace(EvWv’)+noise-z;
constraint(2) = trace(EvWv’)-R(trace(EvW*v’)+noise);
maximize 1/t(log(1+Betaa)/log(2)
subject to
real(constraint)<=0;
Q == hermitian_semidefinite(N+1);
diag(Q) ==1;
cvx_end
At this time, cvx_status: ‘Infeasible’.

I hope you can give me some advice, thanks!

The multiplication sign is omitted from the expression here, but it is actually present.

You have not provided a reproducible problem, so I will refer you to https://yalmip.github.io/debugginginfeasible , which, other than section 1, also applies to CVX.

Is is certainly possible that adding constraints can transform a feasible problem into an infeasible problem. For instance, if the only constraint is x >= 0, the problem is feasible. If the constraint x <= -1 is added, the problem becomes infeasible.

When you are trying to figure out what is going on, do NOT use quiet. Without quiet, the solver and CvX output will be displayed, which might be helpful.

OK, I got it, thank you very much,Mark! I’m going to drop ‘quite’ to find out why it doesn’t work.