The first thing you need to do is to understand what the mathematical statement of the problem is. I don’t.
For instance, what is the right-hand side of the first line of (27), and how does that evaluate to a scalar? is there a misplaced parenthesis and W is supposed to be inside trace?
The right-hand side of the first line of (26) looks like the log of 1 plus scalar*matrix). What is that? It can’t be a matrix log, because it needs to evaluate to a scalar. Or is there a misplaced parenthesis and W is supposed to be inside trace? Is this really log_det? But what to make of 1?
I suggest you simplify to the simplest case, get rid of the confusing subscripts, and write out explicitly what the problem is. You can’t even help yourself until you do that.
Even if this is a convex problem, that doesn’t mean it can be formulated for entry in CVX.
If by chance there is some kind of matrix log, perhaps CVXQUAD can help GitHub - hfawzi/cvxquad: Implementation in MATLAB-based CVX of various convex/concave functions of matrices (matrix geometric means, quantum relative entropy, ...)