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

Gabriel Haeser () and Alberto Ramos ()
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Gabriel Haeser: University of São Paulo
Alberto Ramos: Federal University of Paraná

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 2, No 10, 469-487

Abstract: 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.

Keywords: Multiobjective optimization; Optimality conditions; Constraint qualifications; Regularity; Weak and strong Kuhn–Tucker conditions; 90C29 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-020-01749-z

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