If A is psd, trace(W"*A*W) can be reformulated as square_pos(norm(sqrtm(A)*W,'fro'))
I’ll let you sort through the more complicated cases. Making use of the cyclic permutation invariance of trace may help for more complicated instances of trace of product of matrices. Perhaps matrix_frac will be of some help.
But you need to understand why the problem is convex. And that can’t just be that it is convex because the paper said so.
In the future, please copy and paste code using the Preformatted text icon, rather than posting an image.