{"paper":{"title":"Partial $\\ell_1$ optimization in random linear systems -- finite dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR"],"primary_cat":"math.OC","authors_text":"Mihailo Stojnic","submitted_at":"2016-12-22T04:17:33Z","abstract_excerpt":"In this paper we provide a complementary set of results to those we present in our companion work \\cite{Stojnicl1HidParasymldp} regarding the behavior of the so-called partial $\\ell_1$ (a variant of the standard $\\ell_1$ heuristic often employed for solving under-determined systems of linear equations). As is well known through our earlier works \\cite{StojnicICASSP10knownsupp,StojnicTowBettCompSens13}, the partial $\\ell_1$ also exhibits the phase-transition (PT) phenomenon, discovered and well understood in the context of the standard $\\ell_1$ through Donoho's and our own works \\cite{DonohoPol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07436","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"}