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<p>In this paper, we investigate solution approaches in set optimization that are based on so-called vectorization strategies. Thereby, the original set-valued problems are reformulated as multi-objective optimization problems, whose optimal solution sets approximate those of the original ones in a certain sense. We consider both infinite-dimensional and finite-dimensional vectorization approaches. In doing so, we collect and discuss the most important properties and relationships between the approaches.</p>

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On vectorization strategies in set optimization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月14日

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  • Gabriele Eichfelder,
  • Tobias Gerlach

摘要

In this paper, we investigate solution approaches in set optimization that are based on so-called vectorization strategies. Thereby, the original set-valued problems are reformulated as multi-objective optimization problems, whose optimal solution sets approximate those of the original ones in a certain sense. We consider both infinite-dimensional and finite-dimensional vectorization approaches. In doing so, we collect and discuss the most important properties and relationships between the approaches.