Weak convergence of Markov chain sampling methods and annealing algorithms to diffusions
type: Item
instance of: scholarly article
title: Weak convergence of Markov chain sampling methods and annealing algorithms to diffusions
zbMATH Open document ID: 0696.60064
DOI: 10.1007/BF00940066
author: Saul B. Gelfand
author: Sanjoy K. Mitter
published in: Journal of Optimization Theory and Applications
publication date: 1991-01-01T00:00:00Z
review text: Simulated annealing algorithms have traditionally been developed and analyzed along two distinct lines: metropolis-type Markov chain algorithms and Langevin-type Markov diffusion algorithms. Here, we analyze the dynamics of continuous state Markov chains which arise from a particular implementation of the metropolis and heat-bath Markov chain sampling methods. It is shown that certain continuous time interpolations of the metropolis and heat-bath chains converge weakly to Langevin diffusions running at different time scales. This exposes a close and potentially useful relationship between the Markov chain and diffusion versions of simulated annealing.
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4140955
zbMATH Keywords: global optimization
zbMATH Keywords: simulated annealing algorithms
zbMATH Keywords: Langevin-type Markov diffusion algorithms
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00940066
OpenAlex ID: W1993623764
description: scientific article; zbMATH DE number 4140955