I understand the theoretical expectations, but I’m not sure whether a numerical calculation works or not. Since the integrand of the Ronkin function has a logarithmic singularity on Amoeba, one may get an incorrect result about optimization. Actually, I have failed to evaluate Laplacian (of a-space) for a different model.
But I tried to calculate Laplacian (of x-space) for the present cases, the results look good. So if Optim.jl always gives a correct minimizer, namely a point in the vacuole, one would distinguish the difference. Thank you.