How to find unkown matrix

Hi all,

I’m trying to find a program that finds a solution for this equation:


where A and B are two know matrix and S is the unkown matrix with values in [0, 1].
Is it possible to encode this with cvxpy and find a solution (or multiple solutions)?

Edit: I originally misread the equation and incorrectly said it was linear.

That is s system of quadratic equality constraints, which are non-convex and inconsistent with CVXPY’s or CVX’s DCP rules. Perhaps it can be solved with some add-on to CVXPY, but that is out of scope of this forum, which is for CVX, not CVXPY.