{"paper":{"title":"On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley's Cutting Plane Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ambros Gleixner, Felipe Serrano, Robert Schwarz","submitted_at":"2019-05-20T15:05:12Z","abstract_excerpt":"Recently, Kronqvist et al.~\\cite{KronqvistLundellWesterlund2016} rediscovered the supporting hyperplane algorithm of Veinott~\\cite{Veinott1967} and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs.\n  In this paper we derive the algorithm from a geometric point of view.\n  This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley's cutting plane algorithm~\\cite{J.E.Kelley1960} applied to a particular reformulation of the problem.\n  As a result, we extend the applicability of the supporting hyperplane algorithm to convex pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08157","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"}