Can SVD be used as a constraint?

can CVX accomodate the following problem :

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That looks non-convex to me. Maybe someone more able than me can see a convex reformulation, but I can’t. It doesn’t look like an easy problem to me.

On this forum, it is your responsibility to prove your problem is convex, not just throw random optimization problems at the forum and see which ones turn out to be convex.