LMI constraint is falied

Hello,
Im solving problem

image732×243 8.19 KB

Clearly, we have X==A due to the LMI constraint (33c). But i didnot get the wanted results when i run the matlab code
M=8
cvx_begin sdp
variable A(M+1,M+1)
variable X(M+1,M+1) hermitian
variable Z(M+1,M+1) hermitian
[zeros(M+1,M+1) X-A;
X’-(A)’ Z;]>=0
trace(A)<=1
maximize (trace(X) )
cvx_end

Status: Unbounded
Optimal value (cvx_optval): +Inf
Results show that Z is great, (1e6) and X-A is not small.

Of course by adding constraint Trace(Z)<=100, CVX solved the problem and we get X-A=0 and the results is as follows

Status: Inaccurate/Solved
Optimal value (cvx_optval): +1.00573
But Adding this constraint is not good for my problem considering something else in my problem.

Is there any other way to solve such problem?
Thank you in advance.

(33aq) says minimize trace (X). Your program has maximize(trace(X)) .The CVX result is correct, because (trace of) X and Z can increase together without limit while maintaining feasibility. it appears your program has a “typo” and should instead have minimize(trace(X)).