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Stronger Kuhn-Tucker Type Conditions in Nonsmooth Multiobjective Optimization: Locally Lipschitz Case

Author

Listed:
  • X. F. Li

    (Jilin University
    City University of Hong Kong)

  • J. Z. Zhang

    (City University of Hong Kong)

Abstract

For an inequality constrained nonsmooth multiobjective optimization problem, where the objective and constraint functions are locally Lipschitz, a nonsmooth analogue of the Maeda-type Guignard constraint qualification is given; stronger Kuhn-Tucker type necessary optimality conditions are derived that are expressed in terms of upper convexificators. Moreover, other constraint qualifications sufficient for the nonsmooth analogue are introduced and their relationships are presented.

Suggested Citation

  • X. F. Li & J. Z. Zhang, 2005. "Stronger Kuhn-Tucker Type Conditions in Nonsmooth Multiobjective Optimization: Locally Lipschitz Case," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 367-388, November.
    • Handle: RePEc:spr:joptap:v:127:y:2005:i:2:d:10.1007_s10957-005-6550-9
    DOI: 10.1007/s10957-005-6550-9
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    Citations

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    Cited by:

    1. Min Feng & Shengjie Li & Jie Wang, 2022. "On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 480-503, November.
    2. Peng Zhang & Jin Zhang & Gui-Hua Lin & Xinmin Yang, 2018. "Constraint Qualifications and Proper Pareto Optimality Conditions for Multiobjective Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 763-782, March.
    3. X. F. Li & J. Z. Zhang, 2010. "Existence and Boundedness of the Kuhn-Tucker Multipliers in Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 373-386, May.
    4. Regina S. Burachik & M. M. Rizvi, 2012. "On Weak and Strong Kuhn–Tucker Conditions for Smooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 477-491, November.
    5. Min Feng & Shengjie Li, 2019. "Second-Order Strong Karush/Kuhn–Tucker Conditions for Proper Efficiencies in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 766-786, June.

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