Stochastic optimization on continuous domains with finite-time guarantees by markov chain monte carlo methods

IEEE Transactions on Automatic Control

Volumn 55, Issue 12, 2010, Pages 2858-2863

  Lecchini Visintini, Andrea ^a   Lygeros, John ^b   MacIejowski, Jan M ^c  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b ETH ZURICH   (Switzerland)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Markov chain Monte Carlo (MCMC)

Indexed keywords

CONTINUOUS DOMAIN; MARKOV CHAIN MONTE CARLO; MARKOV CHAIN MONTE CARLO ALGORITHMS; MARKOV CHAIN MONTE CARLO METHOD; STATISTICAL LEARNING THEORY; STOCHASTIC OPTIMIZATION PROBLEMS; STOCHASTIC OPTIMIZATIONS; TIME PERFORMANCE; TOTAL VARIATION NORM;

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; OPTIMIZATION; STOCHASTIC SYSTEMS;

MONTE CARLO METHODS;

EID: 78650028284     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2078170     Document Type: Article

References (32)

1. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science, vol. 220, no. 4598, pp. 671-680, 1983.
2. C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd ed. New York: Springer-Verlag, 2004.
3. M. Vidyasagar, "Randomized algorithms for robust controller synthesis using statistical learning theory," Automatica, vol. 37, no. 10, pp. 1515-1528, 2001. (Pubitemid 32737008)
4. M. Vidyasagar, Learning and Generalization: With Application to Neural Networks, 2nd ed. London, U.K.: Springer-Verlag, 2003.
5. R. Tempo, G. Calafiore, and F. Dabbene, Randomized Algorithms for Analysis and Control of Uncertain Systems. London, U.K.: Springer- Verlag, 2005.
6. T. Alamo, R. Tempo, and E. Camacho, "A randomized strategy for probabilistic solutions of uncertain feasibility and optimization problems," IEEE Trans. Autom. Control, vol. 54, no. 11, pp. 2545-2559, Nov. 2009.
7. S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, 2nd ed. London, U.K.: Springer-Verlag, 2009.
8. J. S. Rosenthal, "Minorization conditions and convergence rates for Markov chain Monte Carlo," J. Amer. Stat. Assoc., vol. 90, no. 430, pp. 558-566, 1995.
9. K. L. Mengersen and R. L. Tweedie, "Rates of convergence of the hastings and metropolis algorithm," Ann. Stat., vol. 24, no. 1, pp. 101-121, 1996.
10. G. O. Roberts and J. S. Rosenthal, "General state space Markov chains and MCMC algorithms," Prob. Surv., vol. 1, pp. 20-71, 2004.
11. A. Shapiro, "Stochastic programming approach to optimization under uncertainty," Math. Program., Ser. B, vol. 112, pp. 183-220, 2008.
12. Y. Nesterov and J.-P. Vial, "Confidence level solutions for stochastic programming," Automatica, vol. 44, no. 6, pp. 1559-1568, 2008.
13. P. Müller, "Simulation based optimal design," in Proc. 6th Valencia Int. Meeting, Bayesian Statistics 6: , J. O. Berger, J. M. Bernardo, A. P. Dawid, and A. F. M. Smith, Eds., Oxford, U.K., 1999, pp. 459-474.
14. A. Doucet, S. Godsill, and P. Robert, "Marginal maximum a posteriori estimation using Markov chain simulation," Statist. Comput., vol. 12, pp. 77-84, 2002.
15. P. Müller, B. Sansó, and M. De Iorio, "Optimal Bayesian design by inhomogeneous Markov Chain simulation," J. Amer. Stat. Assoc., vol. 99, no. 467, pp. 788-798, 2004.
16. A. Lecchini-Visintini, J. Lygeros, and J. M. Maciejowski, "Stochastic Optimization on Continuous DomainsWith Finite-Time Guarantees by Markov Chain Monte Carlo Methods," Tech. Rep., 2010.
17. A. Lecchini-Visintini, J. Lygeros, and J. M. Maciejowski, "Simulated annealing: Rigorous finite-time guarantees for optimization on continuous domains," in Advances in Neural Information Processing Systems 20, J. Platt, D. Koller, Y. Singer, and S. Roweis, Eds. Cambridge, MA: MIT Press, 2008.
18. A. Lecchini-Visintini, J. Lygeros, and J. M. Maciejowski, "On the approximate domain optimization of deterministic and expected value criteria," in Proc. 47th IEEE Conf. Decision Control, Cancun, Mexico, 2008, pp. 4933-4938.
19. T. Rowland, Essential Supremum From MathWorld-A Wolfram Web Resource, created by Eric W. Weisstein [Online]. Available: http:// mathworld.wolfram.com/ EssentialSupremum.html
20. C.-R. Hwang, "Laplacés method revisited:Weak convergence of probability measures," Annu. Prob., vol. 8, no. 6, pp. 1177-1182, 1980.
21. H. Haario and E. Saksman, "Simulated annealing process in general state space," Adv. Appl. Prob., vol. 23, pp. 866-893, 1991.
22. S. B. Gelfand and S. K. Mitter, "Simulated annealing type algorithms for multivariate optimization," Algorithmica, vol. 6, pp. 419-436, 1991.
23. C. Tsallis and D. A. Stariolo, "Generalized simulated annealing," Physica A, vol. 233, pp. 395-406, 1996.
24. M. Locatelli, "Simulated annealing algorithms for continuous global optimization: Convergence conditions," J. Optim. Theory Appl., vol. 104, no. 1, pp. 121-133, 2000.
25. C. Andrieu, L. Breyer, and A. Doucet, "Convergence of simulated annealing using Foster-Lyapunov criteria," J. Appl. Prob., vol. 38, pp. 975-994, 2001.
26. M. Locatelli, "Convergence and first hitting time of simulated annealing algorithms for continuous global optimization," Math. Meth. Oper. Res., vol. 54, pp. 171-199, 2001.
27. S. Rubenthaler, T. Rydén, and M. Wiktorsson, "Fast simulated annealing in with an application to maximum likelihood estimation in state-space models," Stoch. Process. Appl., vol. 119, pp. 1912-1931, 2009.
28. P. M. J. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications. Dordrecht, Holland: D. Reidel Publishing Company, 1987.
29. D. Mitra, F. Romeo, and A. Sangiovanni-Vincentelli, "Convergence and finite-time behavior of simulated annealing," Adv. Appl. Prob., vol. 18, pp. 747-771, 1986.
30. B. Hajek, "Cooling schedules for optimal annealing," Math. Oper. Res., vol. 13, pp. 311-329, 1988.
31. J. Hannig, E. K. P. Chong, and S. R. Kulkarni, "Relative frequencies of generalized simulated annealing," Math. Oper. Res., vol. 31, no. 1, pp. 199-216, 2006.
32. B. Gnedenko, Theory of Probability, 4th ed. New York: Chelsea, 1968.