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Qualitative properties of solutions to set optimization problems

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Abstract

In this paper, we consider set optimization problems involving set relations. Using the well-known KKM-Fan Lemma and relaxed convexity assumptions, we study existence conditions for these problems. Moreover, we introduce parametric nonlinear scalarization functions for sets and study their properties. By utilizing the concerning functions, we investigate relationships between set optimization problems and equilibrium problems. Finally, sufficient conditions for the Hölder continuity of solution maps to such problems via equilibrium problems are established.

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Acknowledgements

The authors wish to thank the Editors and anonymous referees for their helpful remarks and suggestions that helped us significantly improve the paper. The first author is supported by the project under the Grant number B2021-TCT-02 of Ministry of Education and Training of Viet Nam. The second and the last authors are supported by Institute for Computational Science and Technology (ICST) under the Grant number 03/2019/HD-KHCNTT.

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Authors and Affiliations

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

    Lam Quoc Anh

  2. Institute for Computational Science and Technology (ICST), Ho Chi Minh City, Vietnam

    Lam Quoc Anh

  3. Department of Mathematics, Taydo University, Can Tho, Vietnam

    Nguyen Huu Danh

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

    Nguyen Huu Danh

  5. Department of Mathematics, Vo Truong Toan University, Haugiang, Vietnam

    Pham Thanh Duoc

  6. Department of Mathematics, College of Natural Sciences, Cantho University, Can Tho, Vietnam

    Tran Ngoc Tam

Authors
  1. Lam Quoc Anh
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  2. Nguyen Huu Danh
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  3. Pham Thanh Duoc
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  4. Tran Ngoc Tam
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Correspondence to Tran Ngoc Tam.

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Communicated by Gabriel Haeser.

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Anh, L.Q., Danh, N.H., Duoc, P.T. et al. Qualitative properties of solutions to set optimization problems. Comp. Appl. Math. 40, 66 (2021). https://doi.org/10.1007/s40314-021-01458-x

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