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Constraint Qualifications for Karush–Kuhn–Tucker Conditions in Multiobjective Optimization

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  • Gabriel Haeser

    (University of São Paulo)

  • Alberto Ramos

    (Federal University of Paraná)

Abstract

The notion of a normal cone of a given set is paramount in optimization and variational analysis. In this work, we give a definition of a multiobjective normal cone, which is suitable for studying optimality conditions and constraint qualifications for multiobjective optimization problems. A detailed study of the properties of the multiobjective normal cone is conducted. With this tool, we were able to characterize weak and strong Karush–Kuhn–Tucker conditions by means of a Guignard-type constraint qualification. Furthermore, the computation of the multiobjective normal cone under the error bound property is provided. The important statements are illustrated by examples.

Suggested Citation

  • Gabriel Haeser & Alberto Ramos, 2020. "Constraint Qualifications for Karush–Kuhn–Tucker Conditions in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 469-487, November.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:2:d:10.1007_s10957-020-01749-z
    DOI: 10.1007/s10957-020-01749-z
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    References listed on IDEAS

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    Cited by:

    1. Oliver Stein & Maximilian Volk, 2023. "Generalized Polarity and Weakest Constraint Qualifications in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1156-1190, September.

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