Higher-order symmetric duality in nondifferentiable multiobjective programming problems

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 x 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 eta-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. (C) 2003 Elsevier Inc. All rights reserved.