How to impose constraints on a non-standard positive semi-definite matrix

I have a matrix or tensor M that satisfies the following non-standard positivity condition:

This is in general weaker than the matrix M being a positive semidefinite matrix. However, I don’t know how to impose a constraint on M such that it satisfies the above positivity condition. Can CVX+MOSEK (or any other solver) handle this type of constraint? Can it be rephrased as a standard SDP using some transformation on M (tensor factorization or something)? The matrix M in my case is expressed as
Screenshot 2024-05-04 124328

where y_q is the optimization variables and M^q_{ijkl} are known matrices.

Thanks a lot.

I see this has been addressed at .