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Characterization of Norm-Based Robust Solutions in Vector Optimization

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  • Morteza Rahimi

    (University of Tehran)

  • Majid Soleimani-damaneh

    (University of Tehran)

Abstract

In this paper, we study the norm-based robust (efficient) solutions of a vector optimization problem. We define two kinds of non-ascent directions in terms of Clarke’s generalized gradient and characterize norm-based robustness by means of the newly defined directions. This is done under a basic constraint qualification. We extend the provided characterization to vector optimization problems with conic constraints and semi-infinite ones. Moreover, we derive a necessary condition for norm-based robustness utilizing a non-smooth gap function.

Suggested Citation

  • Morteza Rahimi & Majid Soleimani-damaneh, 2020. "Characterization of Norm-Based Robust Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 554-573, May.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:2:d:10.1007_s10957-020-01662-5
    DOI: 10.1007/s10957-020-01662-5
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    References listed on IDEAS

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    Cited by:

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    2. Morteza Rahimi & Majid Soleimani-damaneh, 2023. "Aubin property for solution set in multi-objective programming," Journal of Global Optimization, Springer, vol. 85(2), pages 441-460, February.

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