Higher-order symmetric duality in nondifferentiable multiobjective programming problems

Abstract

In this paper, a pair of nondifferentiable multiobjective programming problems is first formulated, where each of the objective functions contains a support function of a compact convex set in R n . For a differentiable function h :R n×R n→R , we introduce the definitions of the higher-order F-convexity ( F-pseudo-convexity, F-quasi-convexity) of function f :R n→R with respect to h. When F and h are taken certain appropriate transformations, all known other generalized invexity, such as η-invexity, type I invexity and higher-order type I invexity, can be put into the category of the higher-order F-invex functions. Under these the higher-order F-convexity assumptions, we prove the higher-order weak, higher-order strong and higher-order converse duality theorems related to a properly efficient solution.