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On Necessary Conditions For Efficiency In Directionally Differentiable Optimization Problems

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  • Manh-Hung Nguyen

    (THEMA, Université de Cergy-Pontoise , 33 bd du Port, F-95011 Paris Cedex France)

  • Do Van Luu

    (Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi Vietnam)

Abstract

This paper deals with multiobjective programming problems with in- equality, equality and set constraints involving Dini or Hadamard differentiable func- tions. 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, 2008. "On Necessary Conditions For Efficiency In Directionally Differentiable Optimization Problems," THEMA Working Papers 2008-09, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    • Handle: RePEc:ema:worpap:2008-09
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    File URL: http://thema.u-cergy.fr/IMG/documents/2008-09.pdf
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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.
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