{"paper":{"title":"Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"N. X. D. Bao, Tan H. Cao","submitted_at":"2026-06-27T15:05:06Z","abstract_excerpt":"We develop a second-order sensitivity theory for the efficient solution map \\(S\\) of a parametric vector optimization problem \\(\\min_C f(p,x)\\) subject to \\(x\\in H(p)\\). The main point is the passage from efficient values to efficient decisions. Under a value-to-decision error bound (VDB), second-order information for the marginal map \\(\\Phi\\) lifts to a second-order Dini formula for \\(S\\). We first work in the abstract inclusion model \\(x\\in H(p)\\), where outer and inner estimates yield second-order semi-derivability of \\(S\\). We then specialize to structured feasible maps \\(H(p)=\\{x\\in\\Omega"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28965","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/2606.28965/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"}