{"paper":{"title":"Efficient DC Algorithm for Constrained Sparse Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Akiko Takeda, Jun-ya Gotoh, Katsuya Tono","submitted_at":"2017-01-30T06:56:20Z","abstract_excerpt":"We address the minimization of a smooth objective function under an $\\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\\ell_0$-constraint, some efficient algorithms are available; for example, Proximal DC (Difference of Convex functions) Algorithm (PDCA) repeatedly evaluates closed-form solutions of convex subproblems, leading to a stationary point of the $\\ell_0$-constrained problem. However, when the problem has additional convex constraints, they become inefficient because it is difficult to obtain closed-form solutions of the associated subpr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08498","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"}