{"paper":{"title":"Sum-of-squares hierarchies for binary polynomial optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lucas Slot, Monique Laurent","submitted_at":"2020-11-08T17:09:48Z","abstract_excerpt":"We consider the sum-of-squares hierarchy of approximations for the problem of minimizing a polynomial $f$ over the boolean hypercube $\\mathbb{B}^{n}=\\{0,1\\}^n$. This hierarchy provides for each integer $r \\in \\mathbb{N}$ a lower bound $f_{(r)}$ on the minimum $f_{\\min}$ of $f$, given by the largest scalar $\\lambda$ for which the polynomial $f - \\lambda$ is a sum-of-squares on $\\mathbb{B}^{n}$ with degree at most $2r$. We analyze the quality of these bounds by estimating the worst-case error $f_{\\min} - f_{(r)}$ in terms of the least roots of the Krawtchouk polynomials. As a consequence, for fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04027","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.04027/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}