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Fast simulated annealing in with an application to maximum likelihood estimation in state-space models

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  • Rubenthaler, Sylvain
  • Rydén, Tobias
  • Wiktorsson, Magnus

Abstract

We study simulated annealing algorithms to maximise a function [psi] on a subset of . In classical simulated annealing, given a current state [theta]n in stage n of the algorithm, the probability to accept a proposed state z at which [psi] is smaller, is exp(-[beta]n+1([psi](z)-[psi]([theta]n)) where ([beta]n) is the inverse temperature. With the standard logarithmic increase of ([beta]n) the probability , with [psi]max the maximal value of [psi], then tends to zero at a logarithmic rate as n increases. We examine variations of this scheme in which ([beta]n) is allowed to grow faster, but also consider other functions than the exponential for determining acceptance probabilities. The main result shows that faster rates of convergence can be obtained, both with the exponential and other acceptance functions. We also show how the algorithm may be applied to functions that cannot be computed exactly but only approximated, and give an example of maximising the log-likelihood function for a state-space model.

Suggested Citation

  • Rubenthaler, Sylvain & Rydén, Tobias & Wiktorsson, Magnus, 2009. "Fast simulated annealing in with an application to maximum likelihood estimation in state-space models," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1912-1931, June.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:6:p:1912-1931
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    References listed on IDEAS

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    1. M. Locatelli, 2001. "Convergence and first hitting time of simulated annealing algorithms for continuous global optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 171-199, December.
    2. Tsallis, Constantino & Stariolo, Daniel A., 1996. "Generalized simulated annealing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 233(1), pages 395-406.
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    Cited by:

    1. Mathieu Gerber & Luke Bornn, 2017. "Improving simulated annealing through derandomization," Journal of Global Optimization, Springer, vol. 68(1), pages 189-217, May.
    2. Gerber, Mathieu & Bornn, Luke, 2018. "Convergence results for a class of time-varying simulated annealing algorithms," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1073-1094.

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