TAIL PROBABILITY ESTIMATES OF CONTINUOUS-TIME SIMULATED ANNEALING PROCESSES

被引：2

作者：

Tang, Wenpin ^{[1
]}

Zhou, Xun Yu ^{[1
]}

机构：

[1] Columbia Univ, Dept Ind Engn & Operat Res=, New York, NY 10027 USA

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2023年 / 13卷 / 3-4期

关键词：

Simulated annealing; continuous time; convergence rate; Eyring-Kramers law; functional inequalities; overdamped Langevin equation; REVERSIBLE DIFFUSION-PROCESSES; OPTIMIZATION; ASYMPTOTICS; METASTABILITY; CONVERGENCE;

D O I：

10.3934/naco.2022015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the convergence rate of a continuous-time simulated annealing process (X-t; t >= 0) for approximating the global optimum of a given function f. We prove that the tail probability P(f(X-t) > min f + delta) decays polynomial in time with an appropriately chosen cooling schedule of temperature, and provide an explicit convergence rate through a non-asymptotic bound. Our argument applies recent development of the Eyring-Kramers law on functional inequalities for the Gibbs measure at low temperatures.

引用

页码：473 / 485

页数：13

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