Applications of sharp large deviations estimates to optimal cooling schedules
Annales de l'I.H.P. Probabilités et statistiques, Tome 27 (1991) no. 4, pp. 463-518. 
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     author = {Catoni, Olivier},
     title = {Applications of sharp large deviations estimates to optimal cooling schedules},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {463--518},
     publisher = {Gauthier-Villars},
     volume = {27},
     number = {4},
     year = {1991},
     mrnumber = {1141244},
     zbl = {0752.60025},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1991__27_4_463_0/}
}
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Catoni, Olivier. Applications of sharp large deviations estimates to optimal cooling schedules. Annales de l'I.H.P. Probabilités et statistiques, Tome 27 (1991) no. 4, pp. 463-518. http://archive.numdam.org/item/AIHPB_1991__27_4_463_0/

[1] R. Azencott, Simulated Annealing, Séminaire Bourbaki, 40e année, 1987-1988, No 697, June 88. | Numdam | MR | Zbl

[2] O. Catoni, Grandes déviations et décroissance de la température dans les algorithmes de recuit, C. R. Acad. Sci. Paris, T. 307, Series I, 1988, pp. 535-538. | MR | Zbl

[3] O. Catoni, Rough Large Deviations Estimates for Simulated Annealing. Application to Exponential Schedules, preprint, Annals Prob., March 1990 (to appear). | MR | Zbl

[4] O. Catoni, Sharp Large Deviations Estimates for Simulated Annealing Algorithms, preprint, Ann. Inst. Henri Poincaré, Prob. Stat., March 1990 (to appear). | Numdam | MR | Zbl

[5] O. Catoni, Large Deviations for Annealing, Thesis, University Paris-Sud Orsay, March 1990.

[6] T.S. Chiang and Y. Chow, On the Convergence Rate of Annealing Processes, Siam J. Control and Optimization, Vol. 26, No. 6, Nov. 1988. | MR | Zbl

[7] R.L. Dobrushin, Central Limit Theorems for Non-Stationary Markov Chain, I, II (english translation), Theor. Prob. Appl., Vol. 1, 1956, pp. 65-80 and 329-383. | MR | Zbl

[8] M.I. Freidlin and A.D. Wentzell, Random Perturbations of Dynamical Systems, Springer Verlag, 1984. | MR | Zbl

[9] S. Geman and D. Geman, Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images, I.E.E.E. Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, 1984, p. 721-741. | Zbl

[10] B. Gidas, Non-Stationary Markov Chains and Convergence of the Annealing Algorithms, J. Stat. Phys., Vol. 39, 1985, p. 73-131. | Zbl

[11] B. Hajek, Cooling Schedules for Optimal Annealing, Math. Oper. Res., Vol. 13, 1988, pp. 311-329. | MR | Zbl

[12] R.A. Holley, S. Kusuoka and D.W. Stroock, Asymptotics of the Spectral Gap with Applications to the Theory of Simulated Annealing, J. Funct. Anal., Vol. 83, 1989, pp. 333-347. | MR | Zbl

[13] R. Holley and D. Stroock, Simulated Annealing via Sobolev Inequalities, Commun. Math. Phys., Vol. 115, 1988, pp. 553-569. | MR | Zbl

[14] C.R. Hwang and S.J. Sheu, Large Time Behaviours of Perturbed Diffusion Markov Processes with Applications I, II et III, preprints, Institute of Mathematics, Academia Sinica, Tapei, Taiwan, 1986.

[15] C.R. Hwang and S.J. Sheu, Singular Perturbed Markov Chains and Exact Behaviors of Simulated Annealing Process, preprint, J. Theoret. Proba. (submitted). | MR | Zbl

[16] C.R. Hwang and S.J. Sheu, On the Weak Reversibility Condition in Simulated Annealing, preprint, Institute of Mathematics, Academia Sinica, Taipei, Taiwan, 1988. | MR

[17] M. Iosifescu and R. Theodorescu, Random Processes and Learning, Springer Verlag, 1969. | Zbl

[18] D.L. Isaacson and R.W. Madsen, Strongly Ergodic Behaviour for Non-Stationary Markov Processes, Ann. Prob., Vol. 1, 1973, pp. 329-335. | MR | Zbl

[19] S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, Optimization by Simulated Annealing, Science, Vol. 220, 1983, pp. 621-680. | MR

[20] E. Seneta, Non-negative Matrices and Markov Chains, second ed., Springer Verlag, 1981. | Zbl

[21] J.N. Tsitsiklis, A Survey of Large Time Asymptotics of Simulated Annealing Algorithms, in Stochastic Differential Systems, Stochastic Control Theory and Applications, W. FLEMING and P. L. LIONS Eds., I.M.A., Mathematics and its Applications, Vol. 10, Springer Verlag, 1988. | MR | Zbl

[22] J.N. Tsitsiklis, Markov Chains with Rare Transitions and Simulated Annealing, Math. Op. Res., Vol. 14, 1989, p. 1. | MR | Zbl