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New Generalized Invexity for Duality in Multiobjective Programming Problems Involving N-Set Functions

  • S. K. Mishra
  • S. Y. Wang
  • K. K. Lai
  • J. Shi
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 77)

Abstract

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.

Keywords

multiobjective programming n-set function optimality duality generalized convexity 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • S. K. Mishra
    • 1
  • S. Y. Wang
    • 2
  • K. K. Lai
    • 3
  • J. Shi
    • 4
  1. 1.Department of Mathematics, Statistics and Computer ScienceG. B. Pant University of Agriculture and TechnologyIndia
  2. 2.Institute of Systems Science, Academy of Mathematics and Systems SciencesChinese Academy of SciencesChina
  3. 3.Department of Management SciencesCity University of Hong KongHong Kong
  4. 4.Department of Computer Science and Systems EngineeringMuroran Institute of TechnologyJapan

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