The convexity of this problem

Nonconvex
1

I encounter a problem as follows, where Vi is a N*N matrix, other variables are all scalars.

Problem
Problem1866×807 103 KB

I don’t know the convexity of the the constraints since the matrix Vl and Di are coupled in the term marked in the red line. If this term is neither convex nor concave, how to convert this problem into a convex problem (maybe using successive convex approximation) so that CVX can be used?

2

All those constraints are non-convex. This looks like a difficult to solve Nonlinear SDP.

If you want to try SCA you can, but you can look up my previous posts on this forum on SCA. People applying SCA to new problems often are not very successful. Perhaps you can try YALMIP., but Johan will probably tell you this is a nasty problem, and your chance of success might not be good.