Adaptive Newton-based multivariate smoothed functional algorithms for simulation optimization

ACM Transactions on Modeling and Computer Simulation

Volumn 18, Issue 1, 2007, Pages

  Bhatnagar, Shalabh ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Gaussian perturbations; Newton based algorithms; Simulation optimization; Smoothed functional algorithms; Three timescale stochastic approximation

Indexed keywords

APPROXIMATION ALGORITHMS; COMPUTER SIMULATION; FUNCTIONAL ANALYSIS; OPTIMIZATION; PERTURBATION TECHNIQUES; STOCHASTIC MODELS;

GAUSSIAN PERTURBATIONS; SIMULATION OPTIMIZATION; SMOOTHED FUNCTIONAL ALGORITHMS;

ADAPTIVE SYSTEMS;

EID: 38349128504     PISSN: 10493301     EISSN: 15581195     Source Type: Journal    
DOI: 10.1145/1315575.1315577     Document Type: Article

References (31)

1. BERTSEKAS, D. R 1999. Nonlinear Programming. Athena Scientific, Belmont.
2. BERTSEKAS, D. P. AND TSITSIKLIS, J. N. 1989. Parallel and Distributed Computation. Prentice Hall, Englewood Cliffs, NJ.
3. BHATNAGAR, S. 2005. Adaptive multivariate three-timescale stochastic approximation algorithms for simulation based optimization. ACM Trans. Model. Comput. Sim. 15, 1, 74-107.
4. BHATNAGAR, S. AND BORKAR, V. S. 1998. A two time scale stochastic approximation scheme for simulation based parametric optimization. Prob. Eng. Info. Sci. 12, 519-531.
5. BHATNAGAR, S. AND BORKAR, V. S. 2003. Multiscale chaotic SPSA and smoothed functional algorithms for simulation optimization. Simulation 79, 10, 568-580.
6. BHATNAGAR, S., FU, M. C., MARCUS, S. I., AND BHATNAGAR, S. 2001. Two timescale algorithms for simulation optimization of hidden Markov models. IIE Trans. 33, 3, 245-258.
7. BHATNAGAR, S., FU, M. C., MARCUS, S. I., AND WANG, I.-J. 2003. Two-timescale simultaneous perturbation stochastic approximation using deterministic perturbation sequences. ACM Trans Model. Comput. Sim. 13, 2, 180-209.
8. BORKAR, V. S. 1995. Probability Theory: An Advanced Course. Springer Verlag, New York, NY.
9. BRANDIERE, O. 1998. Some pathological traps for stochastic approximation. SIAM J. Contr. Optim. 36, 1293-1314.
10. CASSANDRAS, C. G. 1993. Discrete Event Systems: Modeling and Performance Analysis. Aksen Associates, Boston, MA.
11. CHIN, D. C. 1997. Comparative study of stochastic algorithms for system optimization based on gradient approximation. IEEE Trans. Sys. Man. Cyber. Part B 27, 2, 244-249.
12. FABIAN, V. 1971. Stochastic approximation. In Optimizing Methods in Statistics, J.J.Rustagi, Ed. Academic Press, New York, NY. 439-470.
13. HIRSCH, M. W 1989. Convergent activation dynamics in continuous time networks. New. Netw. 2, 331-349.
14. HO, Y. C. AND CAO, X. R. 1991. Perturbation Analysis of Discrete Event Dynamical Systems. Kluwer, Boston, MA.
15. KATKOVNIK, V. Y. AND KULCHITSKY, Y 1972. Convergence of a class of random search algorithms. Automat. Remote Cont. 8, 1321-1326.
16. KIEFER, E. AND WOLFOWITZ, J. 1952. Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. 23, 462-466.
17. KUSHNER, H. J. AND CLARK, D. S. 1978. Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer Verlag, New York, NY.
18. KUSHNER, H. J. AND YIN, G. G. 1997. Stochastic Approximation Algorithms and Applications. Springer Verlag, New York, NY
19. LASALLE, J. R AND LEFSCHETZ, S. 1961. Stability by Liapunov'3 Direct Method with Applications. Academic Press, New York, NY.
20. L'ECUYER, R AND GLYNN, P. W. 1994. Stochastic optimization by simulation: Convergence proofs for the GI/G/1 queue in steady-state. Manage. Sci. 40, 11, 1562-1578.
21. PEMANTLE, R. 1990. Nonconvergence to unstable points in urn models and stochastic approximations. Ann. Prob. 18, 698-712.
22. ROBBINS, H. AND MONRO, S. 1951. A stochastic approximation method. Ann. Math. Statist. 22, 400-407.
23. RUBINSTEIN, R. Y. 1981. Simulation and the Monte Carlo Method. Wiley, New York, NY.
24. RUPPERT, D. 1985. A Newton-Raphson version of the multivariate Robbins-Monro procedure. Ann. Statist. 13, 236-245.
25. SPALL, J. C. 1992. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Auto. Contr. 37, 3, 332-341.
26. SPALL, J. C. 1997. A one-measurement form of simultaneous perturbation stochastic approximation. Automatica 33, 109-112.
27. SPALL, J. C. 2000. Adaptive stochastic approximation by the simultaneous perturbation method. IEEE Trans. Auto. Contr. 45, 1839-1853.
28. SPALL, J. C. 2006. Convergence analysis for feedback- and weighting-based Jacobian estimates in the adaptive simultaneous perturbation algorithm. In Proceedings of the IEEE Conference on Decision and Control (San Diego, CA, Dec. 13-15). 5669-5674.
29. STYBLINSKI, M. A. AND OPALSKI, L. J. 1986. Algorithms and software tools for IC yield optimization based on fundamental fabrication parameters. IEEE Trans. Comput. Aid. Des. CAD-5, 1, 79-89.
30. STYBLINSKI, M. A. AND TANG, T.-S. 1990. Experiments in nonconvex optimization: Stochastic approximation with function smoothing and simulated annealing. Neur. Netw. 3, 467-483.
31. ZHU, X. AND SPALL, J. C. 2002. A modified second-order SPSA optimization algorithm for finite samples. Int. J. Adapt. Contr. Sign. Process. 16, 397-409.