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Simulated annealing algorithms and Markov chains with rare transitions

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Séminaire de Probabilités XXXIII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1709))

Abstract

In these notes, written for a D.E.A. course at University Paris XI during the first term of 1995, we prove the essentials about stochastic optimisation algorithms based on Markov chains with rare transitions, under the weak assumption that the transition matrix obeys a large deviation principle. We present a new simplified line of proofs based on the Freidlin and Wentzell graphical approach. The case of Markov chains with a periodic behaviour at null temperature is considered. We have also included some pages about the spectral gap approach where we follow Diaconis and Stroock [13] and Ingrassia [23] in a more conventional way, except for the application to non reversible Metropolis algorithms (subsection 6.2.2) where we present an original result.

Date: May 1995, English translation January 1997, in revised form November 1998.

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Authors
  1. Olivier Catoni
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Jacques Azéma Michel Émery Michel Ledoux Marc Yor

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© 1999 Springer-Verlag

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Catoni, O. (1999). Simulated annealing algorithms and Markov chains with rare transitions. In: Azéma, J., Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXIII. Lecture Notes in Mathematics, vol 1709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096510

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  • DOI: https://doi.org/10.1007/BFb0096510

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  • Print ISBN: 978-3-540-66342-3

  • Online ISBN: 978-3-540-48407-3

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