Simulated annealing algorithms and Markov chains with rare transitions

 Access to full text

 Full (PDF)

1. [1] Azencott Robert (1988) Simulated Annealing, Séminaire Bourbaki 40ième année, 1987-1988697. Zbl0687.60086MR992211
2. [2] Azencott Robert (1992) Sequential Simulated Annealing: Speed of Convergence and Acceleration Techniques, in Simulated Annealing: Parallelization Techniques, R. Azencott Ed., Wiley Interscience. Zbl0787.90071MR1188931
3. [3] Azencott Robert (1992) A Common Large Deviations Mathematical Framework for Sequential Annealing and Parallel Annealing, in Simulated Annealing : Parallelization Techniques, R. Azencott Ed., Wiley Interscience. Zbl0787.90072MR1188932
4. [4] Azencott Robertand Graffigne Christine (1992) Parallel Annealing by Periodically Interacting Multiple Searches: Acceleration Rates, in Simulated Annealing : Parallelization Techniques, R. Azencott Ed., Wiley Interscience. Zbl0777.90044MR1188935
5. [5] Catoni Olivier (1991) Exponential Triangular Cooling Schedules for Simulated Annealing Algorithms: a case study, Applied Stochastic Analysis, Proceedings of a US-French Workshop, Rutgers University, April 29 - May 2, 1991, Karatzas I. and Ocone D. eds., Lecture Notes in Control and Information Sciences No 177, Springer Verlag, 1992. MR1169919
6. [6] Catoni Olivier (1992) Rough Large Deviation Estimates for Simulated Annealing: Application to Exponential Schedules, The Annals of Probability, Vol. 20, nb. 3, pp. 1109 - 1146. Zbl0755.60021MR1175253
7. [7] Catoni Olivier, (1998) The Energy Transformation Method for the Metropolis Algorithm Compared with Simulated Annealing. Probab. Theory Related Fields110 (1998), no. 1., pages 69-89. Zbl0897.60078MR1602040
8. [8] Catoni Olivierand Cerf Raphael (1997) The Exit Path of a Markov Chain with Rare Transitions, ESAIM:P&S, vol 1, pp. 95-144, http://www.emath.fr/Maths/Ps/ps.html. Zbl0869.60063
9. [9] Catoni Olivier (1998) Solving Scheduling Problems by Simulated Annealing. SIAM J. Control Optim.36, no. 5, (electronic), pages 1539-1575. Zbl0913.60045MR1626872
10. [10] Catoni Olivier (1996) Metropolis, Simulated Annealing and I.E.T. Algorithms: Theory and Experiments. Journal of Complexity 12, special issue on the conference Foundation of Computational Mathematics, January 5-12 1997, Rio de Janeiro, pages 595-623, December 1996. Zbl0862.68057MR1422728
11. [11] Cot Cécileand Catoni Olivier (1998) Piecewise constant triangular cooling schedules for generalized simulated annealing algorithms. Ann. Appl. Probab.8, no. 2,, pages 375-396. Zbl1053.65500MR1624937
12. [12] Deuschel J.D. and Mazza C. (1994) L2 convergence of time nonhomogeneous Markov processes: I. Spectral Estimates, The annals of Applied Probability, vol. 4, no. 4, 1012-1056. Zbl0819.60063MR1304771
13. [13] Diaconis Persi and Stroock Daniel (1991) Geometric Bounds for Eigenvalues of Markov Chains, The Annals of Applied Probability, Vol. 1, No 1, 36 - 61. Zbl0731.60061MR1097463
14. [14] Duflo M. (1996) Algorithmes Stochastiques, Mathématiques & Applications (Paris), Springer Verlag. Zbl0882.60001
15. [15] Fill J.A. (1991) Eigenvalue bounds on the convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process, Ann. Applied Probab., 1. Zbl0726.60069MR1097464
16. [16] Freidlin, M.I.and Wentzell, A.D. (1984). Random Perturbations of Dynamical Systems. Springer, New York. Zbl0522.60055MR722136
17. [17] Geman S., Geman D., Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images, I.E.E.E. Transactions on Pattern Analysis and Machine Intelligence, 6, 721- 741, 1984. Zbl0573.62030
18. [18] Götze F.. (1991) Rate of Convergence of Simulated Annealing Processes, preprint. MR1106283
19. [19] Graffigne Christine (1992) Parallel Annealing by Periodically Interacting Multiple Searches: An Experimental Study, in Simulated Annealing: Parallelization Techniques, R. Azencott Ed., Wiley Interscience. Zbl0779.90069
20. [20] Holley R. and Stroock D. (1988) Annealing via Sobolev inequalities, Comm. Math. Phys., 115:553-559. Zbl0643.60092MR933455
21. [21] Holley, R.A., Kusuoka, S. and Stroock, D.W. (1989), Asymptotics of the spectral gap with applications to the theory of simulated annealing, Journal of functional analysis, 83, 333-347. Zbl0706.58075MR995752
22. [22] Hwang, C.R.and Sheu, S.J. (1992) Singular perturbed Markov chains and exact behaviour of simulated annealing processes. J. Theoret. Prob., 5, 2, 223-249. Zbl0755.60047MR1157983
23. [23] Ingrassia S. (1994) On the rate of convergence of the Metropolis algorithm and Gibbs sampler by geometric bounds, Ann. Appl. Probab.4, no.2, 347-389. Zbl0802.60061MR1272731
24. [24] Kirchhoff G. (1847) Über die Auflösung der Gleichungen, auf welche man beider Untersuchung der linearen Verteilung galvanischer Ströme gefuhrt wird, Ann. Phys. Chem., 72, pp. 497-508.(English transl. IRE Trans. Circuit Theory CT-5 (1958) 4-7). 
25. [25] Kirkpatrick S., Gelatt C.D. and Vecchi M.P., (1983) Optimization by simulated annealing, Science, 220, 621-680, 1983. Zbl1225.90162MR702485
26. [26] Miclo Laurent (1991) Evolution de l'énergie libre. Application à l'étude de la convergence des algorithmes du recuit simulé. Doctoral Dissertation, Université d'Orsay, February 1991. 
27. [27] Miclo Laurent (1996) Sur les problèmes de sortie discrets inhomogènesAnn. Appl. Probab.6, no 4, 1112-1156. Zbl0870.60062MR1422980
28. [28] Miclo Laurent (1995) Sur les temps d'occupations des processus de Markov finis inhomogènes à basse température, submitted to Stochastics and Stochastics Reports. Zbl1002.60565MR1639780
29. [29] Miclo Laurent (1997) Remarques sur l'hypercontractivité et l'évolution de l'entropie pour des chaines de Markov finies, Séminaire de Probabilités XXXI, Lecture Notes in Mathematics1655, Springer. Zbl0882.60065MR1478724
30. [30] Saloff-Coste, Laurent (1997) Lectures on finite Markov chainsLectures on probability theory and statistics (Saint-Flour, 1996), 301-413, Lecture Notes in Math., 1665, Springer, Berlin. Zbl0885.60061MR1490046
31. [31] Trouvé Alain (1993) Parallélisation massive du recuit simulé, Doctoral Dissertation, Université Paris11, January 5 1993. 
32. [32] Trouvé Alain (1994) Cycle Decomposition and Simulated Annealing, S.I.A.M. J. Control Optim., 34(3), 1996. Zbl0852.60031MR1384962
33. [33] Trouvé Alain (1995) Rough Large Deviation Estimates for the Optimal Convergence Speed Exponent of Generalized Simulated Annealing Algorithms, Ann. Inst. H. Poincaré, Probab. Statist., 32(2), 1996. Zbl0853.60029MR1387393

1. Pierre Del Moral, Laurent Miclo, Dynamiques recuites de type Feynman-Kac : résultats précis et conjectures