Existence of Solutions for Set Optimization Problems with Variable Ordering Structures

Dinh Vinh Hien () and Nguyen Le Hoang Anh ()
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Dinh Vinh Hien: Ho Chi Minh City University of Industry and Trade
Nguyen Le Hoang Anh: University of Science

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 3, No 19, 20 pages

Abstract: 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.

Keywords: Set optimization problem; Variable ordering structure; Proper cone-quasiconvexity; Transfer lower continuity; 49J53; 49K27; 46N10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02823-0

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