{"paper":{"title":"Iterative thresholding algorithm based on non-convex method for modified lp-norm regularization minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Angang Cui, Haiyang Li, Jiajun Xiong, Jigen Peng, Meng Wen","submitted_at":"2018-04-25T06:58:09Z","abstract_excerpt":"Recently, the $\\l_{p}$-norm regularization minimization problem $(P_{p}^{\\lambda})$ has attracted great attention in compressed sensing. However, the $\\l_{p}$-norm $\\|x\\|_{p}^{p}$ in problem $(P_{p}^{\\lambda})$ is nonconvex and non-Lipschitz for all $p\\in(0,1)$, and there are not many optimization theories and methods are proposed to solve this problem. In fact, it is NP-hard for all $p\\in(0,1)$ and $\\lambda>0$. In this paper, we study two modified $\\l_{p}$ regularization minimization problems to approximate the NP-hard problem $(P_{p}^{\\lambda})$. Inspired by the good performance of Half algo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09385","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"}