{"paper":{"title":"Complexity of Unconstrained L_2-L_p Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"cs.CC","authors_text":"Dongdong Ge, Xiaojun Chen, Yinyu Ye, Zizhuo Wang","submitted_at":"2011-05-03T17:24:06Z","abstract_excerpt":"We consider the unconstrained $L_2$-$L_p$ minimization: find a minimizer of $\\|Ax-b\\|^2_2+\\lambda \\|x\\|^p_p$ for given $A \\in R^{m\\times n}$, $b\\in R^m$ and parameters $\\lambda>0$, $p\\in [0,1)$. This problem has been studied extensively in variable selection and sparse least squares fitting for high dimensional data. Theoretical results show that the minimizers of the $L_2$-$L_p$ problem have various attractive features due to the concavity and non-Lipschitzian property of the regularization function $\\|\\cdot\\|^p_p$. In this paper, we show that the $L_q$-$L_p$ minimization problem is strongly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0638","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"}