{"ID":2873088,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.07836","arxiv_id":"2509.07836","title":"Trust-Region Method for Optimization of Set-Valued Maps Given by Finitely Many Functions","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.","short_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 propert...","url_abs":"https://arxiv.org/abs/2509.07836","url_pdf":"https://arxiv.org/pdf/2509.07836v1","authors":"[\"Suprova Ghosh\",\"Debdas Ghosh\",\"Christiane Tammer\",\"Xiaopeng Zhao\"]","published":"2025-09-09T15:11:49Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}