How to use cvx to find E and ϵ that satisfy the following two equations?

This really isn’t a CVX-specific question. Please consider a more general-purpose forum for. In fact it’s not even clear to me this represents a convex set.

Continuing the discussion from How to use cvx to find E and ϵ that satisfy the following two equations?:

In fact,I want to use CVX algorithm to design a WDM, the first equation is its Maxwell’s equations in the frequency domain, and the second equation is its performance limitation. I have read a paper which uses CVX to design a WDM, I’m curious about its algorithm,but I’m confused now. I hope someone could help me to understand it.

Does the paper show the optimization problem which was solved using CVX? Does it show the CVX formulation?

It just give the two equations, and says that they use the the CVX design the WDM’s structure, and gives the result. It doesn’t mentions the specific optimization procedures. The name of the paper is "Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer ".

I’m going to close this one too; please do not post a third. This forum is for support in the use of CVX and TFOCS; and it assumes you are already using it. This post simply does not qualify. Please go back to the authors of the paper to find out how they converted this problem to a CVX-compatible form.