{"paper":{"title":"Convergence rate analysis of a sequential convex programming method with line search for a class of constrained difference-of-convex optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Peiran Yu, Ting Kei Pong, Zhaosong Lu","submitted_at":"2020-01-20T07:11:44Z","abstract_excerpt":"In this paper, we study the sequential convex programming method with monotone line search (SCP$_{ls}$) in [46] for a class of difference-of-convex (DC) optimization problems with multiple smooth inequality constraints. The SCP$_{ls}$ is a representative variant of moving-ball-approximation-type algorithms [6,10,13,54] for constrained optimization problems. We analyze the convergence rate of the sequence generated by SCP$_{ls}$ in both nonconvex and convex settings by imposing suitable Kurdyka-Lojasiewicz (KL) assumptions. Specifically, in the nonconvex settings, we assume that a special poten"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.06998","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.06998/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}