{"paper":{"title":"The LP-Newton Method and Conic Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Francesco Silvestri, Gerhard Reinelt","submitted_at":"2016-11-28T17:50:41Z","abstract_excerpt":"We propose that the LP-Newton method can be used to solve conic LPs over a conic box, whenever linear optimization over an otherwise unconstrained conic box is easy. In particular, if $\\leq_\\mathcal{K}$ is the partial order induced by a proper convex cone $\\mathcal{K}$, then optimizing a linear function over the intersection of $[{l},{u}]_\\mathcal{K}=\\{{l}\\leq_\\mathcal{K} {x}\\leq_\\mathcal{K}{u}\\}$ and an affine subspace can be done with this method whenever optimizing a linear function over $[{l},{u}]_{\\mathcal{K}}$ is efficient.\n  This generalizes the result for the case of $\\mathcal{K}=\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09260","kind":"arxiv","version":2},"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"}