Higher Order Invexity and Duality in Mathematical Programming

Abstract

In 1975 Mangasarian formulated a higher order dual to the nonlinear programming problem: Minimize {\textbrokenbar}(x) Subject to g(x) ≥ 0. He did not prove weak duality find hence only gave a limited strong duality theorem. Subsequently, Mond and Weir gave conditions for full duality find, as well, formulated other higher order duals. Here we give invexity type conditions under which duality holds between the above problem and various higher order dual programming problems.