{"paper":{"title":"Fenchel-Moreau Conjugation Inequalities with Three Couplings and Application to Stochastic Bellman Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean-Philippe Chancelier (CERMICS), Michel de Lara (CERMICS)","submitted_at":"2018-04-09T14:52:21Z","abstract_excerpt":"Given two couplings between \"primal\" and \"dual\" sets,   we prove a general implication   that relates an inequality involving \"primal\" sets   to a reverse inequality involving the \"dual\" sets.%  More precisely,  let be given two \"primal\" sets $\\PRIMAL$, $\\PRIMALBIS$and two \"dual\" sets $\\DUAL$, $\\DUALBIS$, together with two {coupling} functions  \\(\\PRIMAL \\overset{\\coupling}{\\leftrightarrow} \\DUAL \\) and  \\(\\PRIMALBIS \\overset{\\couplingbis}{\\leftrightarrow} \\DUALBIS \\).  We define a new coupling \\(\\SumCoupling{\\coupling}{\\couplingbis} \\)  between the \"primal\" product set~$\\PRIMAL \\times \\PRIMAL"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03034","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"}