{"paper":{"title":"On a decomposition formula for the proximal operator of the sum of two convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fabien Caubet, Lo\\\"ic Bourdin, Samir Adly","submitted_at":"2017-07-26T15:53:34Z","abstract_excerpt":"The main result of the present theoretical paper is an original decomposition formula for the proximal operator of the sum of two proper, lower semicontinuous and convex functions $f$ and $g$. For this purpose, we introduce a new operator, called $f$-proximal operator of $g$ and denoted by $\\mathrm{prox}^f_g$, that generalizes the classical notion. Then we prove the decomposition formula $\\mathrm{prox}_{f+g} = \\mathrm{prox}_f \\circ \\mathrm{prox}^f_g$. After collecting several properties and characterizations of $\\mathrm{prox}^f_g$, we prove that it coincides with the fixed points of a generali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08509","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"}