Convergence of simulated annealing using Foster-Lyapunov criteria

Journal of Applied Probability

Volumn 38, Issue 4, 2001, Pages 975-994

  Andrieu, Christophe ^a   Breyer, Laird A ^b   Doucet, Arnaud ^c  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b LANCASTER UNIVERSITY   (United Kingdom)

^c UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Foster Lyapunov; Markov chain Monte Carlo; Nonhomogeneous Markov chain; Optimization; Simulated annealing

Indexed keywords

EID: 0035528756     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1011994186     Document Type: Article

References (24)

1. ANDRIEU, C. AND DOUCET, A. (2000). Simulated annealing for maximum a posteriori parameter estimation of hidden Markov models. IEEE Trans. Inf. Theory 46, 994-1004.
2. BILLINGSLEY, P. (1985). Probability and Measure, 2nd edn. John Wiley, Chichester.
3. FORT, G. AND MOULINES, É. (2000). V-subgeometric ergodicity for a Hastings-Metropolis algorithm. Statist. Prob. Lett. 49, 401-410.
4. FORT, G., MOULINES, É. AND ROBERTS, G. O. (2001). A geometrically ergodic hybrid sampler for sub-exponential densities. Submitted.
5. d. SIAM J. Control Optimization 31, 111-131.
6. GEMAN, S. AND GEMAN, D. (1984). Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intellig. 6, 721-741.
7. HAARIO, A. AND SAKSMAN, E. (1991). Simulated annealing in general state space. Adv. Appl. Prob. 23, 866-893.
8. HWANG, C. (1980). Laplace's method revisited: weak convergence of probability measures. Ann. Prob. 8, 1177-1182.
9. JARNER, S. F. AND HANSEN, E. (1998). Geometric ergodicity of Metropolis algorithms. Stoch. Process. Appl. 85, 341-361.
10. JARNER, S. F. AND ROBERTS, G. (2001). Polynomial convergence rates of Markov chains. To appear in Ann. Appl. Prob.
11. LINDVALL, T. (1992). Lectures on the Coupling Method. John Wiley, New York.
12. LOCATELLI, M. (2000). Simulated annealing algorithms for continuous global optimization: convergence conditions. J. Optimization Theory Appl. 104, 121-133.
13. MENGERSEN, K. L. AND TWEEDIE, R. L. (1994). Rates of convergence of the Hastings and Metropolis algorithm. Ann. Statist. 24, 101-121.
14. MEYN, S. P. AND TWEEDIE, R. L. (1993). Markov Chains and Stochastic Stability. Springer, Berlin.
15. MITRA, D., ROMEO, F. AND SANGIOVANNI-VINCENTELLI, A. (1986). Convergence and finite-time behavior of simulated annealing. Adv. Appl. Prob. 18, 747-771.
16. ROBERTS, G. O. AND ROSENTHAL, J. S. (1998). Two convergence properties of hybrid samplers. Ann. Appl. Prob. 8, 397-407.
17. ROBERTS, G. O. AND TWEEDIE, R. L. (1996). Exponential convergence of Langevin diffusions and their discrete approximations. Bernoulli 2, 341-364.
18. ROBERTS, G. O. AND TWEEDIE, R. L. (1996). Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83, 96-110.
19. ROBERTS, G. O. AND TWEEDIE, R. L. (1999). Bounds on regeneration times and convergence rates for Markov chains. Stock. Process. Appl. 80, 211-229.
20. ROSENTHAL, J. S. (1995). Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Statist. Assoc. 90, 558-566.
21. TWEEDIE, R. AND STRAMER, O. (1999). Langevin-type models I: diffusions with given stationary distributions, and their discretizations. Methodology Comput. Appl. Prob. 1, 283-306.
22. TWEEDIE, R. AND STRAMER, O. (1999). Langevin-type models II: self-targeting candidates for MCMC algorithms. Methodology Comput. Appl. Prob. 1, 307-328.
23. TIERNEY, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22, 1701-1762.
24. VAN LAARHOVEN, P. J. AND ARTS, E. H. L. (1987). Simulated Annealing: Theory and Applications. Reidel, Amsterdam.