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Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation

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Abstract

This article investigates stability conditions for set optimization problems with the set less order relation in the senses of Panilevé–Kuratowski and Hausdorff convergence. Properties of various kinds of convergences for elements in the image space are discussed. Taking such properties into account, formulations of internal and external stability of the solutions are studied in the image space in terms of the convergence of a solution sets sequence of perturbed set optimization problems to a solution set of the given problem.

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Acknowledgements

The authors are very grateful to the Editor and anonymous Referees for their helpful remarks and suggestions that helped us significantly improve the presentation of the paper. The research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2020.11 and JSPS KAKENHI Grant Number 19K03637.

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Authors and Affiliations

  1. Department of Mathematics, Teacher College, Cantho University, Can Tho, Vietnam

    Lam Quoc Anh

  2. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Tran Quoc Duy

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Tran Quoc Duy

  4. Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam

    Dinh Vinh Hien

  5. Department of Mathematics, Ho Chi Minh City University of Food Industry, Ho Chi Minh City, Vietnam

    Dinh Vinh Hien

  6. Department of Mathematics, Shimane University, Matsue, Shimane, 690-8504, Japan

    Daishi Kuroiwa

  7. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand

    Narin Petrot

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  1. Lam Quoc Anh
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  2. Tran Quoc Duy
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  3. Dinh Vinh Hien
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  4. Daishi Kuroiwa
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  5. Narin Petrot
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Correspondence to Tran Quoc Duy.

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Communicated by Anil Aswani.

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Anh, L.Q., Duy, T.Q., Hien, D.V. et al. Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation. J Optim Theory Appl 185, 416–432 (2020). https://doi.org/10.1007/s10957-020-01657-2

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  • DOI: https://doi.org/10.1007/s10957-020-01657-2

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