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Generalized (F,ρ)-Convexity and Duality in Nonsmooth Problems of Multiobjective Optimization

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  • S. Nobakhtian

    (University of Isfahan)

Abstract

A mixed-type dual for a nonsmooth multiobjective optimization problem with inequality and equality constraints is formulated. We obtain weak and strong duality theorems for a mixed-type dual without requiring the regularity assumptions and the nonnegativeness of the Lagrange multipliers associated to the equality constraints. We apply also a nonsmooth constraint qualification for multiobjective programming to establish strong duality results. In this case, our constraint qualification assures the existence of positive Lagrange multipliers associated with the vector-valued objective function.

Suggested Citation

  • S. Nobakhtian, 2008. "Generalized (F,ρ)-Convexity and Duality in Nonsmooth Problems of Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 61-68, January.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:1:d:10.1007_s10957-007-9319-5
    DOI: 10.1007/s10957-007-9319-5
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    References listed on IDEAS

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    1. VIAL, Jean-Philippe, 1982. "Strong convexity of sets and functions," LIDAM Reprints CORE 475, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. X. F. Li, 2000. "Constraint Qualifications in Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 106(2), pages 373-398, August.
    3. Vial, Jean-Philippe, 1982. "Strong convexity of sets and functions," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 187-205, January.
    4. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    5. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Thai Chuong & Do Kim, 2014. "Optimality conditions and duality in nonsmooth multiobjective optimization problems," Annals of Operations Research, Springer, vol. 217(1), pages 117-136, June.

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