{"paper":{"title":"Shannon-and von neumann-entropy regularizations of linear and semidefinite programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean B Lasserre (LAAS-POP, Saroj Prasad Chhatoi (LAAS-POP), TSE-R)","submitted_at":"2025-03-31T07:49:48Z","abstract_excerpt":"We consider the LP in standard form min {c T x\\,: Ax = b; x $\\ge$ 0} and inspired by $\\epsilon$-regularization in Optimal Transport, we introduce its $\\epsilon$-regularization ''min {c T x + $\\epsilon$ f (x)\\,: Ax = b; x $\\ge$ 0}'' via the (convex) Boltzmann-Shannon entropy f (x)\\,:= i x i ln x i . We also provide a similar regularization for the semidefinite program ''min {Tr(C $\\bullet$ X)\\,: A(X) = b; X 0}'' but with now the so-called Von Neumann entropy, as in Quantum Optimal Transport. Importantly, both are not barriers of the LP and SDP cones respectively. We show that this problem admit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.23815","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.23815/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"}