A Vectorization Scheme for Nonconvex Set Optimization Problems
Optimization and Control
2021-07-27 v1
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.
Cite
@article{arxiv.2107.12274,
title = {A Vectorization Scheme for Nonconvex Set Optimization Problems},
author = {Gabriele Eichfelder and Ernest Quintana and Stefan Rocktäschel},
journal= {arXiv preprint arXiv:2107.12274},
year = {2021}
}