MINIMAX PROGRAMMING WITH $(G, \ALPHA)$-INVEXTY

Abstract

In this paper, we deal with the minimax programming (P) under the differentiable  $(G, \alpha)$-invexity which was proposed in [J. Nonlinear Anal. Optim. 2(2): 305-315]. With the help of auxiliary programming problem $(G-P)$, some new Kuhn-Tucker necessary conditions, namely for G-Kuhn-Tucker necessary conditions, is presented for the minimax programming (P). Also G-Karush-Kuhn-Tucker sufficient conditions under $(G, \alpha)$-invexity assumption are obtained for the minimax programming (P). Making use of these optimality conditions, we construct a dual problem (DI) for (P) and establish weak, strong and strict converse duality theorems between problems (P)and (DI).