A Vectorization Scheme for Nonconvex Set Optimization Problems
A Vectorization Scheme for Nonconvex Set Optimization Problems
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DOI：
10.1137/21m143683x
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Gabriele Eichfelder;Ernest Quintana;Stefan Rocktäschel
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文献类型：
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作者：
Gabriele Eichfelder;Ernest Quintana;Stefan Rocktäschel
本文研究了关于下集少关系的集合优化问题的一种求解方法。这种方法可以作为利用多目标优化中已建立的求解器数值求解集合优化问题的基础。我们的策略包括导出多目标优化问题的参数族，其最优解集在特定意义上近似于具有任意精度的集值问题的最优解集。我们还研究了特定的集值映射类，对于这些集值映射，其相应的集优化问题等价于生成族中的多目标优化问题。令人惊讶的是，这包括具有凸图的集值映射。
In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution sets approximate, in a specific sense, that of the set-valued problem with arbitrary accuracy. We also examine particular classes of set-valued mappings for which the corresponding set optimization problem is equivalent to a multiobjective optimization problem in the generated family. Surprisingly, this includes set-valued mappings with a convex graph.