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

Citation data:

Stochastic Processes and their Applications, ISSN: 0304-4149

Publication Year:
2017
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DOI:
10.1016/j.spa.2017.07.007
Author(s):
Mathieu Gerber, Luke Bornn
Publisher(s):
Elsevier BV
Tags:
Mathematics
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article description
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.

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