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On alternative theorems and necessary conditions for efficiency

Author

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  • Do Van Luu

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

  • Manh-Hung Nguyen

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

Abstract

In this paper, we establish theorems of the alternative for a system described by inequalities, equalities and an inclusion, which are generalizations of Tucker's classical theorem of the alternative, and develop Kuhn-Tucker necessary conditions for efficiency to mathematical programs in normed spaces involving inequality, equality and set constraints with positive Lagrange multipliers of all the components of objective functions.

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  • Do Van Luu & Manh-Hung Nguyen, 2006. "On alternative theorems and necessary conditions for efficiency," Post-Print halshs-00112454, HAL.
    • Handle: RePEc:hal:journl:halshs-00112454
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00112454
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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. T. Illés & G. Kassay, 1999. "Theorems of the Alternative and Optimality Conditions for Convexlike and General Convexlike Programming," Journal of Optimization Theory and Applications, Springer, vol. 101(2), pages 243-257, May.
    3. 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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