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Optimality and error bound for set optimization with application to uncertain multi-objective programming

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  • Wenyan Han

    (North Minzu University)

  • Guolin Yu

    (North Minzu University)

Abstract

This paper deals with optimality conditions and error bound for a set optimization problem with the set less order relation. We introduce two kinds of vectorization functions by using the classical oriented distance function, and discuss their properties with respect to the set less order relation. By virtue of the image space analysis, necessary and sufficient optimality conditions for the weak s-minimal solution are established. We propose a regular weak separation function, which is utilized to construct a gap function and an error bound for the set optimization problem. Problems of uncertain multi-objective programming, shortest path and medical image registration are examined as applications of the results established in the paper.

Suggested Citation

  • Wenyan Han & Guolin Yu, 2024. "Optimality and error bound for set optimization with application to uncertain multi-objective programming," Journal of Global Optimization, Springer, vol. 88(4), pages 979-998, April.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:4:d:10.1007_s10898-023-01327-3
    DOI: 10.1007/s10898-023-01327-3
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    References listed on IDEAS

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    1. Elisa Caprari & Lorenzo Cerboni Baiardi & Elena Molho, 2022. "Scalarization and robustness in uncertain vector optimization problems: a non componentwise approach," Journal of Global Optimization, Springer, vol. 84(2), pages 295-320, October.
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    3. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 609-636, June.
    4. Jiawei Chen & Shengjie Li & Zhongping Wan & Jen-Chih Yao, 2015. "Vector Variational-Like Inequalities with Constraints: Separation and Alternative," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 460-479, August.
    5. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis—Part III: Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 660-678, June.
    6. Qamrul Hasan Ansari & Elisabeth Köbis & Pradeep Kumar Sharma, 2019. "Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 817-839, June.
    7. B. Jiménez & V. Novo & A. Vílchez, 2020. "Characterization of set relations through extensions of the oriented distance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 89-115, February.
    8. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis—Part II: Duality and Penalization," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 637-659, June.
    9. Qamrul Hasan Ansari & Pradeep Kumar Sharma, 2022. "Some Properties of Generalized Oriented Distance Function and their Applications to Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 247-279, June.
    10. Yang-Dong Xu & Cheng-Ling Zhou & Sheng-Kun Zhu, 2021. "Image Space Analysis for Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 311-343, October.
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