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<p>We revisit two types of constrained vector optimization problems driven by set-valued maps, where the domination structure is defined by a cone-valued map. Within the framework of variable domination structures, we demonstrate that the approaches used in the literature cover each other. This observation enables us to design unified methods for deriving necessary optimality conditions in both cases. Our results rely on key concepts such as the Extremal Principle and the inherent incompatibility between openness and efficiency, encompassing several well-known assertions in this area of research.</p>

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Vector Optimization with Variable Domination Structure: A Unifying Approach

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月13日

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  • Marius Durea,
  • Radu Strugariu,
  • Christiane Tammer

摘要

We revisit two types of constrained vector optimization problems driven by set-valued maps, where the domination structure is defined by a cone-valued map. Within the framework of variable domination structures, we demonstrate that the approaches used in the literature cover each other. This observation enables us to design unified methods for deriving necessary optimality conditions in both cases. Our results rely on key concepts such as the Extremal Principle and the inherent incompatibility between openness and efficiency, encompassing several well-known assertions in this area of research.