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Optimality Conditions for Vector Optimization Problems

Author

Listed:
  • N. J. Huang

    (Sichuan University)

  • J. Li

    (China West Normal University)

  • S. Y. Wu

    (National Cheng-Kung University
    National Center for Theoretical Sciences)

Abstract

In this paper, some necessary and sufficient optimality conditions for the weakly efficient solutions of vector optimization problems (VOP) with finite equality and inequality constraints are shown by using two kinds of constraints qualifications in terms of the MP subdifferential due to Ye. A partial calmness and a penalized problem for the (VOP) are introduced and then the equivalence between the weakly efficient solution of the (VOP) and the local minimum solution of its penalized problem is proved under the assumption of partial calmness.

Suggested Citation

  • N. J. Huang & J. Li & S. Y. Wu, 2009. "Optimality Conditions for Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 323-342, August.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:2:d:10.1007_s10957-009-9514-7
    DOI: 10.1007/s10957-009-9514-7
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    References listed on IDEAS

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    5. A. D. Ioffe, 1984. "Necessary Conditions in Nonsmooth Optimization," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 159-189, May.
    6. Dehui Yuan & Altannar Chinchuluun & Xiaoling Liu & Panos M. Pardalos, 2007. "Optimality Conditions and Duality for Multiobjective Programming Involving (C, α, ρ, d) type-I Functions," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 73-87, Springer.
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    Cited by:

    1. Marius Durea & Radu Strugariu & Christiane Tammer, 2013. "Scalarization in Geometric and Functional Vector Optimization Revisited," Journal of Optimization Theory and Applications, Springer, vol. 159(3), pages 635-655, December.
    2. Elena Constantin, 2019. "Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 75(1), pages 111-129, September.
    3. T. Antczak, 2016. "Optimality Conditions in Quasidifferentiable Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 708-725, November.
    4. Jiawei Chen & Yu-Hong Dai, 2023. "Multiobjective optimization with least constraint violation: optimality conditions and exact penalization," Journal of Global Optimization, Springer, vol. 87(2), pages 807-830, November.
    5. Shaojian Qu & Mark Goh & Soon-Yi Wu & Robert Souza, 2014. "Multiobjective DC programs with infinite convex constraints," Journal of Global Optimization, Springer, vol. 59(1), pages 41-58, May.

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