An Extremum Principle for Smooth Problems

Abstract

We derive an extremum principle. It can be treated as an intermediate result between the celebrated smooth-convex extremum principle due to Ioffe and Tikhomirov and the Dubovitskii–Milyutin theorem. The proof of this principle is based on a simple generalization of the Fermat’s theorem, the smooth-convex extremum principle and the local implicit function theorem. An integro-differential example illustrating the new principle is presented.