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.
Journal of Applied Probability and Advances in Applied Probability have for four decades provided a forum for original research and reviews in applied probability, mapping the development of probability theory and its applications to physical, biological, medical, social and technological problems. Their wide readership includes leading researchers in the many fields in which stochastic models are used, including operations research, telecommunications, computer engineering, epidemiology, financial mathematics, information systems and traffic management. Advances includes a section dedicated to stochastic geometry and its statistical applications.
The Applied Probability Trust is a non-profit publishing foundation established in 1964 to promote study and research in the mathematical sciences. Its titles Journal of Applied Probability and Advances in Applied Probability were the first in the subject. The regular publications of the Trust also include The Mathematical Scientist, and the student mathematical magazine Mathematical Spectrum. The Trust publishes occasional special volumes on applied probability and related subjects.
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