Higher-order symmetric duality in nondifferentiable multiobjective programming problems

By Xiuhong Chen. 2004

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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 Rn. 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.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/de5b783112a1601ae2c7d50c699ac3ad52fe6fe0