Invex function

A function f from Rⁿ to R is an invex function if there exists a vector valued function g such that

$f(x)-f(u)\geq g(x,u)\cdot \nabla f'(u)$

for all x and u.

Invex functions were introduced by Hanson as a generalization of convex functions. Hanson proves that a function is invex if and only if every stationary point is a global minimum.