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Convergence theorems for a class of simulated annealing algorithms on ℝd

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

Published online by Cambridge University Press:  14 July 2016

Claude J. P. Bélisle
Claude J. P. Bélisle*
Affiliation:
University of Michigan
*
∗ Postal address: Department of Statistics, University of Michigan, Ann Arbor, MI 48109–1027, USA.
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Abstract

We study a class of simulated annealing algorithms for global minimization of a continuous function defined on a subset of We consider the case where the selection Markov kernel is absolutely continuous and has a density which is uniformly bounded away from 0. This class includes certain simulated annealing algorithms recently introduced by various authors. We show that, under mild conditions, the sequence of states generated by these algorithms converges in probability to the global minimum of the function. Unlike most previous studies where the cooling schedule is deterministic, our cooling schedule is allowed to be adaptive. We also address the issue of almost sure convergence versus convergence in probability.

Keywords

MONTE CARLO METHODSOPTIMIZATIONADAPTIVE COOLING SCHEDULE

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 885 - 895
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported in part by NATO Collaborative Research Grant No. 0119/89.

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