How to write the following function f(x,y) in CVX form

[Michal_Adamaszek]

Was discussed in the past. Convex and “looks conic”, but actually without a known conic representation.

How to express the function "1/(exp(x^2)-1)"

This t\geq \frac{1}{e^x-1},\quad x>0 is equivalent to 1\geq e^{-x}+\frac{1}{1+t} which can be written almost verbatim 1 >= exp(-x) + inv_pos(1+t) However your variant with x^2 seems much harder. Maybe you can reformulate the whole model somehow to avoid the square.