{"paper":{"title":"Quasi-Newton Method for Set Optimization Problems with Set-Valued Mapping Given by Finitely Many Vector-Valued Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Anshika, Debdas Ghosh, Jen-Chih Yao, Xiaopeng Zhao","submitted_at":"2024-12-29T15:01:40Z","abstract_excerpt":"In this article, we propose a quasi-Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The set-valued objective mapping under consideration is given by a finite number of vector-valued functions that are twice continuously differentiable. To find the necessary optimality condition for weak minimal points with the help of the proposed quasi-Newton method, we use the concept of partition and formulate a family of vector optimization problems. The evaluation of necessary optimality condition for finding the weakl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04711","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.04711/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}