I am currently trying to build some procedures in Maple that calculate the Legendre-Fenchel transformation for functions that are convex, nonconvex, differentiable and non-differentiable functions. I seem to be ok in the convex case, but cannot seem to find a way of getting Maple to calculate this transformation symbolically for nonconvex functions (both differentiable and non-differentiable). It appears to me that the only way to deal with these cases is to calculate the transform numerically for some given value (k).
I appreciate this is a fairly obscure topic so there is a link to some background information at the bottom of this post. If anyone has any thoughts or suggestions I would be really interested to hear them.