{"paper":{"title":"Box constrained $\\ell_1$ optimization in random linear systems -- asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.OC"],"primary_cat":"math.PR","authors_text":"Mihailo Stojnic","submitted_at":"2016-12-20T20:23:38Z","abstract_excerpt":"In this paper we consider box constrained adaptations of $\\ell_1$ optimization heuristic when applied for solving random linear systems. These are typically employed when on top of being sparse the systems' solutions are also known to be confined in a specific way to an interval on the real axis. Two particular $\\ell_1$ adaptations (to which we will refer as the \\emph{binary} $\\ell_1$ and \\emph{box} $\\ell_1$) will be discussed in great detail. Many of their properties will be addressed with a special emphasis on the so-called phase transitions (PT) phenomena and the large deviation principles "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06835","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"}