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Duality and Its Applications to Optimality Conditions with Nonsolid Cones

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Abstract

In this paper, we first establish the weak, strong, and converse duality theorems for a pair of primal–dual problems in set-valued optimization concerning Q-efficient solutions. Then, duality theorems for quasi-relative efficient solutions and Henig efficient solutions are implied with Q being appropriately chosen cones. Finally, their applications to optimality conditions in the Kuhn–Tucker type are obtained.

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Acknowledgments

This study was supported by the project of the Moravian-Silesian Region, Czech Republic reg. no. 02692/2014/RRC. The author is grateful to two anonymous referees for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Ostrava, 30. Dubna 22, 70103, Ostrava, Czech Republic

    Nguyen Le Hoang Anh

  2. Department of Optimization and System Theory, University of Science, Vietnam National University Ho Chi Minh City, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Vietnam

    Nguyen Le Hoang Anh

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  1. Nguyen Le Hoang Anh
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Correspondence to Nguyen Le Hoang Anh.

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Communicated by Rosihan M. Ali.

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Anh, N.L.H. Duality and Its Applications to Optimality Conditions with Nonsolid Cones. Bull. Malays. Math. Sci. Soc. 41, 1061–1076 (2018). https://doi.org/10.1007/s40840-016-0375-6

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  • DOI: https://doi.org/10.1007/s40840-016-0375-6

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