{"paper":{"title":"Box constrained $\\ell_1$ 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":"2016-12-20T20:34:01Z","abstract_excerpt":"Our companion work \\cite{Stojnicl1BnBxasymldp} considers random under-determined linear systems with box-constrained sparse solutions and provides an asymptotic analysis of a couple of modified $\\ell_1$ heuristics adjusted to handle such systems (we refer to these modifications of the standard $\\ell_1$ as binary and box $\\ell_1$). Our earlier work \\cite{StojnicISIT2010binary} established that the binary $\\ell_1$ does exhibit the so-called phase-transition phenomenon (basically the same phenomenon well-known through earlier considerations to be a key feature of the standard $\\ell_1$, see, e.g. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06839","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"}