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(Q*v*W*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(E*v*W*v’)-R*(trace(E*v*W*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!