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Second-Order Conditions for Efficiency in Nonsmooth Multiobjective Optimization Problems

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  • T. Maeda

    (Kanazawa University)

Abstract

In this paper, we are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. We introduce a second-order constraint qualification, which is a generalization of the Abadie constraint qualification and derive second-order Kuhn-Tucker type necessary conditions for efficiency under the constraint qualification. Moreover, we give some conditions which ensure the constraint qualification holds.

Suggested Citation

  • T. Maeda, 2004. "Second-Order Conditions for Efficiency in Nonsmooth Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 521-538, September.
    • Handle: RePEc:spr:joptap:v:122:y:2004:i:3:d:10.1023_b:jota.0000042594.46637.b4
    DOI: 10.1023/B:JOTA.0000042594.46637.b4
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    Cited by:

    1. P. Q. Khanh & N. D. Tuan, 2007. "Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 341-357, June.
    2. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    3. W. Song & G. M. Yao, 2008. "Homotopy Method for a General Multiobjective Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 139-153, July.
    4. Vsevolod I. Ivanov, 2015. "Second-Order Optimality Conditions for Vector Problems with Continuously Fréchet Differentiable Data and Second-Order Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 777-790, September.
    5. Anulekha Dhara & Aparna Mehra, 2013. "Second-Order Optimality Conditions in Minimax Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 567-590, March.
    6. 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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