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Applications of sharp large deviations estimates to optimal cooling schedules. (English) Zbl 0752.60025
This paper is a sequel to [author, ibid. 27, No. 3, 291-383 (1991; Zbl 0746.60024)]. It has been drawn from the author’s thesis at the University Paris-Sud Orsay, March 1990, supervised by R. Azencott. Aim of this second part is to study applications of large deviations to cooling systems of the critical type, i.e. $1/T\sb n=(1/d) \ln n+B+o(1)$, where $d$ is Hajek’s critical depth. Although quasi-equilibrium is not maintained for such schedules, it turns out that the law of the system is not “too far” from quasi-equilibrium if $B$ is small. However, if $B$ is above some critical value, convergence rates of the annealing algorithm can be made arbitrarily poor by increasing $B$. Sharp large deviations estimates are needed in order to obtain the desired results. - -- Contents: 1. Estimation of the probability of the critical cycle. 2. Asymptotics of the law of the system. 3. Triangular cooling schedules. 4. The optimization problem far from the horizon.

60F10Large deviations
60J10Markov chains (discrete-time Markov processes on discrete state spaces)
93E25Computational methods in stochastic control
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