{"paper":{"title":"Characterizing weak solutions for vector optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Dang H. Long, Marco A. L\\'opez, Miguel A. Goberna, Nguyen Dinh","submitted_at":"2016-02-10T13:33:57Z","abstract_excerpt":"This paper provides characterizations of the weak solutions of optimization problems where a given vector function $F,$ from a decision space $X$ to an objective space $Y$, is \"minimized\" on the set of elements $x\\in C$ (where $C\\subset X$ is a given nonempty constraint set), satisfying $G\\left( x\\right) \\leqq_{S}0_{Z},$ where $G$ is another given vector function from $X $ to a constraint space $Z$ with positive cone $S$. The three spaces $X,Y,$ and $Z$ are locally convex Hausdorff topological vector spaces, with $Y$ and $Z$ partially ordered by two convex cones $K$ and $S,$ respectively, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03367","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":""},"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"}