convexchecker

It checks real valued multidimensional function, whether it is convex.

This script may be easily converted to a function which could be an extremely useful subroutine in optimization problems to check whether the objective function is globally convex. It may also be used to derive the expressions for gradient and Hessian of the given multidimensional real valued function along with giving their values at the point entered. It uses Sylvester's criterion to check positive definiteness of the Hessian, as it checks whether all the principal minors of the Hessian are positive.