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Convergence Theorems for a Class of Simulated Annealing Algorithms on Rd

Claude J. P. Bélisle
Journal of Applied Probability
Vol. 29, No. 4 (Dec., 1992), pp. 885-895
DOI: 10.2307/3214721
Stable URL: http://www.jstor.org/stable/3214721
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Convergence Theorems for a Class of Simulated Annealing Algorithms on Rd
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Abstract

We study a class of simulated annealing algorithms for global minimization of a continuous function defined on a subset of Rd. We consider the case where the selection Markov kernel is absolutely continuous and has a density which is uniformly bounded away from 0. This class includes certain simulated annealing algorithms recently introduced by various authors. We show that, under mild conditions, the sequence of states generated by these algorithms converges in probability to the global minimum of the function. Unlike most previous studies where the cooling schedule is deterministic, our cooling schedule is allowed to be adaptive. We also address the issue of almost sure convergence versus convergence in probability.

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