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Optimality Conditions and Duality for Multiobjective Programming Involving (C, α, ρ, d) type-I Functions

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Generalized Convexity and Related Topics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 583))

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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Hanshan Teachers’ College, Chaozhou, Guangdong Province, China

    Dehui Yuan & Xiaoling Liu

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611, USA

    Altannar Chinchuluun & Panos M. Pardalos

Authors
  1. Dehui Yuan
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  2. Altannar Chinchuluun
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  3. Xiaoling Liu
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  4. Panos M. Pardalos
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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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