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<p>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.</p>

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Existence of Solutions for Set Optimization Problems with Variable Ordering Structures

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Dinh Vinh Hien,
  • Nguyen Le Hoang Anh

摘要

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.