{"paper":{"title":"Lifting $\\ell_q$-optimization thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.OC"],"primary_cat":"cs.IT","authors_text":"Mihailo Stojnic","submitted_at":"2013-06-17T08:54:47Z","abstract_excerpt":"In this paper we look at a connection between the $\\ell_q,0\\leq q\\leq 1$, optimization and under-determined linear systems of equations with sparse solutions. The case $q=1$, or in other words $\\ell_1$ optimization and its a connection with linear systems has been thoroughly studied in last several decades; in fact, especially so during the last decade after the seminal works \\cite{CRT,DOnoho06CS} appeared. While current understanding of $\\ell_1$ optimization-linear systems connection is fairly known, much less so is the case with a general $\\ell_q,0<q<1$, optimization. In our recent work \\cit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3976","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"}