Further Generalizations of Convexity in Mathematical Programming

Abstract

The Kuhn-Tucker conditions for the existence of solutions to inequality constrained minimization problems are sufficient conditions when all the functions involved are convex. Various concepts such as pseudo-convexity and quasi-convexity have been introduced for the purpose of weakening this limitation of convexity in mathematical programming. Still wider classes of functions are introduced in this paper and applied in Kunh-Tucker theory and in duality theory.