{"paper":{"title":"Global Optimization via Schr{\\\"o}dinger-F{\\\"o}llmer Diffusion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jerry Zhijian Yang, Lican Kang, Xiliang Lu, Yin Dai, Yuling Jiao","submitted_at":"2021-10-31T03:54:26Z","abstract_excerpt":"We study the problem of finding global minimizers of $V(x):\\mathbb{R}^d\\rightarrow\\mathbb{R}$ approximately via sampling from a probability distribution $\\mu_{\\sigma}$ with density $p_{\\sigma}(x)=\\dfrac{\\exp(-V(x)/\\sigma)}{\\int_{\\mathbb R^d} \\exp(-V(y)/\\sigma) dy }$ with respect to the Lebesgue measure for $\\sigma \\in (0,1]$ small enough.\n  We analyze a sampler based on the Euler-Maruyama discretization of the Schr{\\\"o}dinger-F{\\\"o}llmer diffusion processes with stochastic approximation under appropriate assumptions on the step size $s$ and the potential $V$.\n  We prove that the output of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.00402","kind":"arxiv","version":6},"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/2111.00402/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"}