Minimizing the largest singular value of e^D*M*e^-D

I am trying to use CVX to minimize sigma_max(e^DMe^-D) where M is a predetermined matrix and D is diagonal. It is known that this problem is convex ( however, so far, I have not been able to formulate it in a way that fits DCP rule set. I was wondering if you can suggest a way.

Sorry, I don’t think it is possible.