{"paper":{"title":"Fast simulated annealing in $\\R^d$ and an application to maximum likelihood estimation","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Magnus Wiktorsson (CENTRE for Mathematical Sciences), Sylvain Rubenthaler (JAD), Tobias Ryd\\'en (CENTRE for Mathematical Sciences)","submitted_at":"2006-09-13T12:44:39Z","abstract_excerpt":"Using classical simulated annealing to maximise a function $\\psi$ defined on a subset of $\\R^d$, the probability $\\p(\\psi(\\theta\\_n)\\leq \\psi\\_{\\max}-\\epsilon)$ tends to zero at a logarithmic rate as $n$ increases; here $\\theta\\_n$ is the state in the $n$-th stage of the simulated annealing algorithm and $\\psi\\_{\\max}$ is the maximal value of $\\psi$. We propose a modified scheme for which this probability is of order $n^{-1/3}\\log n$, and hence vanishes at an algebraic rate. To obtain this faster rate, the exponentially decaying acceptance probability of classical simulated annealing is replac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609353","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"}