{"paper":{"title":"Proximal alternating minimization and projection methods for nonconvex problems. An approach based on the Kurdyka-Lojasiewicz inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antoine Soubeyran, Hedy Attouch, Jerome Bolte, Patrick Redont","submitted_at":"2008-01-11T13:54:05Z","abstract_excerpt":"We study the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: $L(x,y)=f(x)+Q(x,y)+g(y)$, where $f:\\R^n\\rightarrow\\R\\cup{+\\infty}$ and $g:\\R^m\\rightarrow\\R\\cup{+\\infty}$ are proper lower semicontinuous functions, and $Q:\\R^n\\times\\R^m\\rightarrow \\R$ is a smooth $C^1$ function which couples the variables $x$ and $y$. The algorithm can be viewed as a proximal regularization of the usual Gauss-Seidel method to minimize $L$. We work in a nonconvex setting, just assuming that the function $L$ satisfies the Kurdyka-\\L ojasiewicz "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1780","kind":"arxiv","version":3},"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"}