Mean square rates of convergence in the continuous time simulated annealing algorithm on \({\mathbb{R}}^ d\)
type: Item
instance of: scholarly article
title: Mean square rates of convergence in the continuous time simulated annealing algorithm on \({\mathbb{R}}^ d\)
zbMATH Open document ID: 0638.60069
DOI: 10.1016/0196-8858(88)90005-X
author: Larry Goldstein
published in: Advances in Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: To locate a global minimum value of a function V at \(\theta\) one may employ the simulated annealing algorithm, a gradient descent procedure modified to climb uphill in order to escape local minima. The continuous version of the simulated annealing procedure is given by the diffusion \[ dX_ t=-\nabla V(X_ t) dt+\sigma_ t dW_ t. \] The paper shows under suitable assumptions on V if \[ \sigma^ 2_ t=c/\log (t+2), \] then there exist positive constants \(c_ 1\) and \(c_ 2\) such that \[ c_ 2\leq \sqrt{\log t} E| X_ t-\theta |^ 2\leq c_ 1 \] for sufficiently large t.
reviewed by: Eckhard Platen
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 4040977
zbMATH Keywords: simulated annealing algorithm
zbMATH Keywords: escape local minima
MaRDI profile type: Publication
cites work: Q4404205
cites work: Limit set of inhomogeneous Ornstein-Uhlenbeck processes, destabilization and annealing
cites work: The N-City Travelling Salesman Problem: Statistical Mechanics and the Metropolis Algorithm
cites work: Diffusion for Global Optimization in $\mathbb{R}^n $
cites work: Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
cites work: Diffusions for Global Optimization
cites work: Nonstationary Markov chains and convergence of the annealing algorithm
cites work: Mapping DNA by stochastic relaxation
cites work: Optimization by Simulated Annealing
cites work: Asymptotic Global Behavior for Stochastic Approximation and Diffusions with Slowly Decreasing Noise Effects: Global Minimization via Monte Carlo
Recommended article: Convergence theorems for a class of simulated annealing algorithms on ℝd
Recommended article: On the simulated annealing in \(\mathbb{R}^d\)
Recommended article: On the convergence rate of the simulated annealing algorithm
Recommended article: Q4878351
Recommended article: Convergence of Gibbs measures associated with simulated annealing: The case of distance squared
Recommended article: Q5751696
Recommended article: On the convergence of stationary distributions in simulated annealing algorithms
Recommended article: Convergence and finite-time behavior of simulated annealing
Recommended article: Convergence of the simulated annealing algorithm for continuous global optimization
description: scientific article; zbMATH DE number 4040977