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

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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.

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Notes

  1. We sometimes use the term strong Pareto to refer to a Pareto point only to emphasize the contrast with the notion of a weak Pareto point. This is not related to the notion of strong minimality defined in [25].

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Authors and Affiliations

  1. Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil

    Gabriel Haeser

  2. Department of Mathematics, Federal University of Paraná, Paraná, Brasil

    Alberto Ramos

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  1. Gabriel Haeser
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  2. Alberto Ramos
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Correspondence to Alberto Ramos.

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Communicated by Alexey F. Izmailov.

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Haeser, G., Ramos, A. Constraint Qualifications for Karush–Kuhn–Tucker Conditions in Multiobjective Optimization. J Optim Theory Appl 187, 469–487 (2020). https://doi.org/10.1007/s10957-020-01749-z

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