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Convergence of simulated annealing using Foster-Lyapunov criteria

Part of: Probabilistic methods, simulation and stochastic differential equations Markov processes

Published online by Cambridge University Press:  14 July 2016

Christophe Andrieu ,
Laird A. Breyer  and
Arnaud Doucet
Christophe Andrieu*
Affiliation:
University of Bristol
Laird A. Breyer*
Affiliation:
Lancaster University
Arnaud Doucet*
Affiliation:
University of Melbourne
*
∗ Postal address: Department of Mathematics, Statistics Group, University of Bristol, University Walk, Bristol BS8 1TW, UK. Email address: [email protected]
∗∗ Postal address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YF, UK.
∗∗∗ Postal address: Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, Victoria 3010, Australia.
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Abstract

Simulated annealing is a popular and much studied method for maximizing functions on finite or compact spaces. For noncompact state spaces, the method is still sound, but convergence results are scarce. We show here how to prove convergence in such cases, for Markov chains satisfying suitable drift and minorization conditions.

Keywords

Simulated annealingMarkov chain Monte CarlooptimizationFoster-Lyapunovnonhomogeneous Markov chain

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 65C40: Computational Markov chains
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 975 - 994
Copyright
Copyright © by the Applied Probability Trust 2001 

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