{"paper":{"title":"Splitting forward-backward penalty scheme for constrained variational problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Juan Peypouquet, Marc-Olivier Czarnecki, Nahla Noun","submitted_at":"2014-08-05T14:01:51Z","abstract_excerpt":"We study a forward backward splitting algorithm that solves the variational inequality \\begin{equation*} A x +\\nabla \\Phi(x)+ N_C (x) \\ni 0 \\end{equation*} where $H$ is a real Hilbert space, $A: H\\rightrightarrows H$ is a maximal monotone operator, $\\Phi: H\\to\\mathbb{R}$ is a smooth convex function, and $N_C$ is the outward normal cone to a closed convex set $C\\subset H$. The constraint set $C$ is represented as the intersection of the sets of minima of two convex penalization function $\\Psi_1:H\\to\\mathbb{R}$ and $\\Psi_2: H\\to\\mathbb{R}\\cup \\{+\\infty\\}$. The function $\\Psi_1$ is smooth, the fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0974","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"}