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Higher-order Karush–Kuhn–Tucker optimality conditions for set-valued optimization with nonsolid ordering cones

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Abstract

In this paper, we consider higher-order Karush–Kuhn–Tucker optimality conditions in terms of radial derivatives for set-valued optimization with nonsolid ordering cones. First, we develop sum rules and chain rules in the form of equality for radial derivatives. Then, we investigate set-valued optimization including mixed constraints with both ordering cones in the objective and constraint spaces having possibly empty interior. We obtain necessary conditions for quasi-relative efficient solutions and sufficient conditions for Pareto efficient solutions. For the special case of weak efficient solutions, we receive even necessary and sufficient conditions. Our results are new or improve recent existing ones in the literature.

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Acknowledgments

This research was supported by Vietnam National University-Hochiminh City under grant number B2015-28-03. The authors are grateful to the editor and an anonymous referee for their valuable comments and remarks which have helped them to improve the paper.

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Authors and Affiliations

  1. Department of Optimization and System Theory, University of Science, Vietnam National University Hochiminh City, 227 Nguyen Van Cu, District 5, Hochiminh City, Vietnam

    Nguyen Le Hoang Anh

  2. Department of Mathematics, International University, Vietnam National University Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam

    Phan Quoc Khanh

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  1. Nguyen Le Hoang Anh
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Le Hoang Anh, N., Khanh, P.Q. Higher-order Karush–Kuhn–Tucker optimality conditions for set-valued optimization with nonsolid ordering cones. Positivity 21, 931–953 (2017). https://doi.org/10.1007/s11117-016-0444-y

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