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Convergence results for a class of time-varying simulated annealing algorithms

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  • Gerber, Mathieu
  • Bornn, Luke

Abstract

We provide a set of conditions which ensure the almost sure convergence of a class of simulated annealing algorithms on a bounded set X⊂Rd based on a time-varying Markov kernel. The class of algorithms considered in this work encompasses the one studied in Bélisle (1992) and Yang (2000) as well as its derandomized version recently proposed by Gerber and Bornn (2016). To the best of our knowledge, the results we derive are the first examples of almost sure convergence results for simulated annealing based on a time-varying kernel. In addition, the assumptions on the Markov kernel and on the cooling schedule have the advantage of being trivial to verify in practice.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:4:p:1073-1094
    DOI: 10.1016/j.spa.2017.07.007
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    References listed on IDEAS

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    1. L. Ingber, 1989. "Very fast simulated re-annealing," Lester Ingber Papers 89vf, Lester Ingber.
    2. M. Locatelli, 2000. "Simulated Annealing Algorithms for Continuous Global Optimization: Convergence Conditions," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 121-133, January.
    3. 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.
    4. R. L. Yang, 2000. "Convergence of the Simulated Annealing Algorithm for Continuous Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 691-716, March.
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