{"paper":{"title":"Linear Perturbations of Quasiconvex Functions and Convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Khanh Pham Duy, Marc Lassonde","submitted_at":"2015-02-13T06:43:03Z","abstract_excerpt":"Let $E$ be a real vector space with dual space $E^*$ and let $C\\subset E$ be a convex subset with more than one point. Let $f : C\\to\\mathbb{R}$ be a function satisfying a mild stability property at 'flat' points of the (relative) boundary of $C$. We show that $f$ is convex if and only if for some linear form $c^*$ on $E$ not constant on $C$, the function $f+\\lambda c^*$ is quasiconvex for all $\\lambda\\in\\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03897","kind":"arxiv","version":2},"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"}