New Generalized Invexity for Duality in Multiobjective Programming Problems Involving N-Set Functions
In this paper, we introduce four types of generalized convexity for an n -set function and discuss optimality and duality for a multiobjective programming problem involving n -set functions. Under some mild assumption on the new generalized convexity, we present a few optimality conditions for an efficient solution and a weakly efficient solution to the problem. Also we prove a weak duality theorem and a strong duality theorem for the problem and its Mond-Weir and general Mond-Weir dual problems respectively.
Keywordsmultiobjective programming n-set function optimality duality generalized convexity
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