Conic representation convex function with arsinh


I would like to give a conic representation, with exponential and quadratic cones as available by Mosek, to the following convex function :

f(x,y)=(x^2 + y^2)^0.5 - (x^2 + (ky)^2)^0.5 + x * (arsinh(x/(ky)) - arsinh(x/y))

where 0<k<1. Do you think it is possible ? Thanks.


When you graphed the function in say matlab, then did it look convex?

Ok sorry, I have forgotten to precise that y>0 in f(x,y). It seems to be convex in this range.

It might be convex.

If there is a comic representation, this might be an example which in order to find it, would need the hypothetical computer algebra capability alluded to in
Ph.D. Thesis idea: Next generation of CVX or CVXPY which automatically figues out reformulations using "computer algebra" techniques