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arXiv · 2107.12274

A Vectorization Scheme for Nonconvex Set Optimization Problems

Gabriele Eichfelder·Ernest Quintana·Stefan Rocktäschel
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Abstract

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.

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Gabriele Eichfelder, Ernest Quintana, Stefan Rocktäschel. 2021-07-26. A Vectorization Scheme for Nonconvex Set Optimization Problems. https://arxiv.org/abs/2107.12274

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