How should I write the following positive semidefinite constraint in cvx?

[Mark_L_Stone]

@tbchen wrote “it is a negative number, and I want it to be positive.”

I want a billion dollars. That doesn’t mean I’m going to get it.

Does your problem have a constraint that requires the optimum to be positive? CVX and Mosek aren’t mind readers, and won’t insert constraints not specified in the problem.

It appears you are using unsafeguarded (no line search or trust region) Scucessive Convex Approximation.

The result obtained using the SeDuMi solver is inaccurate. The optimal solution is not as good as before the optimization.

Unsafeguarded (no line search or trust region)Successive Convex Approximation (SCA) or generally, alternating variables optimization are unreliable. It might not descend (for minimization problem), i.e., iterates could get worse. It might not converge to anything; and if it does converge, it might not be to a local optimum of the original problem, let alone a global optimum. The solution of successive iterations, and therefore subproblem inputs, can become wilder and wilder, until at some point …

I will leave it to you to investigate whether the overall algorithm you are using might be easily repairable with the incorporation of an additional constraint in the sub-problems. I offer no opinion on the merits of whatever paper or book you found this algorithm in, or on the merits of the algorithms itself. But I will say as a general matter that there are SCA algorithms proposed in many papers published in even prestigious journals which are unreliable and which might not have passed my scrutiny had I been a referee or editor of the paper (I am tough, but fair)…