In vector calculus, an invex function is a differentiable function ƒ from Rn to R for which there exists a vector valued function g such that
for all x and u.
Invex functions were introduced by Hanson as a generalization of convex functions. Ben-Israel and Mond provided a simple proof that a function is invex if and only if every stationary point is a global minimum.
Hanson also showed that if the objective and the constraints of an optimization problem are invex with respect to the same function g(x, u), then the Karush–Kuhn–Tucker conditions are sufficient for a global minimum.
A slight generalization of invex functions called Type 1 invex functions are the most general class of functions for which the Karush–Kuhn–Tucker conditions are necessary and sufficient for a global minimum.