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On necessary conditions for efficiency in directionally differentiable optimization problems

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  • Manh-Hung Nguyen

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Do Van Luu

    (Institut de Mathématiques [Hanoi] - Académie des Sciences et Techniques)

Abstract

This paper deals with multiobjective programming problems with inequality, equality and set constraints involving Dini or Hadamard differentiable functions. A theorem of the alternative of Tucker type is established and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.

Suggested Citation

  • Manh-Hung Nguyen & Do Van Luu, 2006. "On necessary conditions for efficiency in directionally differentiable optimization problems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00118977, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00118977
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00118977
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    References listed on IDEAS

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    1. X. F. Li, 2000. "Constraint Qualifications in Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 373-398, August.
    2. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
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