Abstract
Simulated annealing algorithms have traditionally been developed and analyzed along two distinct lines: Metropolis-type Markov chain algorithms and Langevin-type Markov diffusion algorithms. Here, we analyze the dynamics of continuous state Markov chains which arise from a particular implementation of the Metropolis and heat-bath Markov chain sampling methods. It is shown that certain continuous-time interpolations of the Metropolis and heat-bath chains converge weakly to Langevin diffusions running at different time scales. This exposes a close and potentially useful relationship between the Markov chain and diffusion versions of simulated annealing.
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Communicated by R. Conti
The research reported here has been supported by the Whirlpool Foundation, by the Air Force Office of Scientific Research under Contract 89-0276, and by the Army Research Office under Contract DAAL-03-86-K-0171 (Center for Intelligent Control Systems).
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Gelfand, S.B., Mitter, S.K. Weak convergence of Markov chain sampling methods and annealing algorithms to diffusions. J Optim Theory Appl 68, 483–498 (1991). https://doi.org/10.1007/BF00940066
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DOI: https://doi.org/10.1007/BF00940066