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Existence of Solutions for Set Optimization Problems with Variable Ordering Structures

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  • Dinh Vinh Hien

    (Ho Chi Minh City University of Industry and Trade)

  • Nguyen Le Hoang Anh

    (University of Science
    Vietnam National University)

Abstract

This article focuses on the existence of solutions to set optimization problems based on variable ordering structures. First, the relationships among different solution types of such problems are disscused. Next, we establish sufficient conditions for the existence of efficient solutions by constructing appropriate level sets and utilizing the semicontinuity properties of objective mappings. Furthermore, we investigate the conditions necessary for the existence of ideal solutions, which require the proper cone-quasiconvexity of the objective mapping. Finally, our analysis extends to weak efficient solutions, applying transfer lower continuity assumptions. This study is novel and enhances the understanding of the results regarding the existence of solutions to set optimization problems in the literature.

Suggested Citation

  • Dinh Vinh Hien & Nguyen Le Hoang Anh, 2025. "Existence of Solutions for Set Optimization Problems with Variable Ordering Structures," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-20, December.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:3:d:10.1007_s10957-025-02823-0
    DOI: 10.1007/s10957-025-02823-0
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