Summary
In this chapter, we present a unified formulation of generalized convex functions. Based on these concepts, sufficient optimality conditions for a nondifferentiable multiobjective programming problem are presented. We also introduce a general Mond-Weir type dual problem of the problem and establish weak duality theorem under generalized convexity assumptions. Strong duality result is derived using a constraint qualification for nondifferentiable multiobjective programming problems.
This research of the first two authors is partially supported in part by NSF, Air Force, and CRDF grants. The research of the third author is partially supported by National Natural Science Foundation of China under Project 10201017.
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Yuan, D., Chinchuluun, A., Liu, X., Pardalos, P.M. (2007). Optimality Conditions and Duality for Multiobjective Programming Involving (C, α, ρ, d) type-I Functions. In: Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, vol 583. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-37007-9_3
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DOI: https://doi.org/10.1007/978-3-540-37007-9_3
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