I want to minimize a complicated objective function, and I'm not sure if it is convex.  Is there a nice algorithm that attempts to prove that it is not convex?  Of course the algorithm could fail to prove this, in which case I would not know if it is convex or not, and this is OK; I just want to try to rule out convexity before I spend a lot of time trying to analytically determine whether the objective function is convex, for example by trying to rewrite the problem in a standard form known to be convex.  One quick test would be to try to minimize from various starting points and if multiple local minima are found in this manner then it is not convex.  But I was wondering if there is a better algorithm that was designed with this goal in mind.
How to intellligently attempt to rule out convexity?
convex optimization