Trust-Region Method for Optimization of Set-Valued Maps Given by Finitely Many Functions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908527887384576 |
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| author | Ghosh, Suprova Ghosh, Debdas Tammer, Christiane Zhao, Xiaopeng |
| author_facet | Ghosh, Suprova Ghosh, Debdas Tammer, Christiane Zhao, Xiaopeng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trust-Region Method for Optimization of Set-Valued Maps Given by Finitely Many Functions Ghosh, Suprova Ghosh, Debdas Tammer, Christiane Zhao, Xiaopeng Optimization and Control 90C20, 90C30, 90C46, 49M37, 65K05 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. |
| title | Trust-Region Method for Optimization of Set-Valued Maps Given by Finitely Many Functions |
| topic | Optimization and Control 90C20, 90C30, 90C46, 49M37, 65K05 |
| url | https://arxiv.org/abs/2509.07836 |