{"paper":{"title":"Comparison of Lasserre's measure--based bounds for polynomial optimization to bounds obtained by simulated annealing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Etienne de Klerk, Monique Laurent","submitted_at":"2017-03-02T12:10:28Z","abstract_excerpt":"Comparison of Lasserre's measure--based bounds for polynomial optimization to bounds obtained by simulated annealing. We consider the problem of minimizing a continuous function $f$ over a compact set $\\mathbf{K}$. We compare the hierarchy of upper bounds proposed by Lasserre in [{\\em SIAM J. Optim.} $21(3)$ $(2011)$, pp. $864-885$] to bounds that may be obtained from simulated annealing.\n  We show that, when $f$ is a polynomial and $\\mathbf{K}$ a convex body, this comparison yields a faster rate of convergence of the Lasserre hierarchy than what was previously known in the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00744","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"}