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Karush–Kuhn–Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints

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Abstract

This paper concentrates on studying multiobjective semi-infinite programming with vanishing constraints. Firstly, the necessary and sufficient Karush–Kuhn–Tucker optimality conditions for multiobjective semi-infinite programming with vanishing constraints are considered. Then, we formulate Wolfe and Mond–Weir type dual problems and establish duality relations under convexity assumptions. Some examples are proposed to verify our results.

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Acknowledgements

The author would like to thank the Editors for the help in the processing of the article. The author is very grateful to the Anonymous Referees for the very valuable remarks, which helped to improve the paper. This work is partially supported by Can Tho University. A part of this paper was completed when the author stayed as a research visitor at Vietnam Institute for Advanced Study in Mathematics (VIASM), whose hospitality is gratefully acknowledged.

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  1. Department of Mathematics, College of Natural Sciences, Can Tho University, Can Tho, 900000, Vietnam

    Le Thanh Tung

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Tung, L.T. Karush–Kuhn–Tucker optimality conditions and duality for multiobjective semi-infinite programming with vanishing constraints. Ann Oper Res 311, 1307–1334 (2022). https://doi.org/10.1007/s10479-020-03742-1

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