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