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arXiv · 2509.07836

Trust-Region Method for Optimization of Set-Valued Maps Given by Finitely Many Functions

Suprova Ghosh·Debdas Ghosh·Christiane Tammer·Xiaopeng Zhao
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Abstract

In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is globally convergent and has the descent property. To ensure the descent property, a new rule of trust-region reduction ratio is introduced for the considered set-valued maps. In the derived method, to find the sequence of iteration points, we need to perform one iteration of a different vector optimization problem at each iteration. Thus, the derived technique is found to be not a straight extension of that for vector optimization. The effectiveness of the proposed algorithm is reported through performance profiles of the proposed approach with the existing methods on various test examples. A list of test problems for set optimization is also provided.

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Suprova Ghosh, Debdas Ghosh, Christiane Tammer, Xiaopeng Zhao. 2025-09-09. Trust-Region Method for Optimization of Set-Valued Maps Given by Finitely Many Functions. https://arxiv.org/abs/2509.07836

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