results in the CVX error:
Cannot perform the operation: {log-affine} .* {real affine}

I think that the objective is convex since it is the affine composition of convex function. Is there a way to describe this according to the DCP rules?

I’d like to see a more thorough proof of convexity. In particular you claim it is an affine composition of a convex function… that’s not a well-posed claim, actually, but perhaps you mean the composition of a convex function and an affine function. What are those two functions, specifically?

Per the FAQ: Do not trust your intuition alone on convexity. Prove it. In fact, in order to use CVX, for reasons we explain below, CVX only accepts models that can be proven convex using only the rules in CVX’s DCP ruleset. If you have not yet done that, go do that now and come back to this FAQ.