Newton-based simultaneous perturbation stochastic approximation

Lecture Notes in Control and Information Sciences

Volumn 434, Issue , 2013, Pages 105-131

  Bhatnagar, S ^a   Prasad, H ^a   Prashanth, L ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

COSTS; OPTIMIZATION; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

ESTIMATION SCHEMES; EXPECTED COSTS; LONG-RUN AVERAGE COST; MUTUALLY INDEPENDENTS; SIMULTANEOUS PERTURBATION STOCHASTIC APPROXIMATION; SPSA ALGORITHMS; SYMMETRIC PERTURBATIONS;

PERTURBATION TECHNIQUES;

EID: 84930504143     PISSN: 01708643     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-4471-4285-0_7     Document Type: Chapter

References (13)

1. Bertsekas, D.P.: Nonlinear Programming. Athena Scientific, Belmont (1999)
2. Bhatnagar, S.: Adaptive multivariate three-timescale stochastic approximation algorithms for simulation based optimization. ACM Transactions on Modeling and Computer Simulation 15(1), 74-107 (2005)
3. Borkar, V.S.: Stochastic Approximation: A Dynamical Systems Viewpoint. Cambridge University Press and Hindustan Book Agency (Jointly Published), Cambridge and New Delhi (2008)
4. Fabian, V.: Stochastic approximation. In: Rustagi, J.J. (ed.) Optimizing Methods in Statistics, pp. 439-470. Academic Press, New York (1971)
5. Kushner, H.J., Clark, D.S.: Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer, New York (1978)
6. Kushner, H.J., Yin, G.G.: Stochastic Approximation Algorithms and Applications. Springer, New York (1997)
7. Lasalle, J.P., Lefschetz, S.: Stability by Liapunov’s Direct Method with Applications. Academic Press, New York (1961)
8. Patro, R.K., Bhatnagar, S.: A probabilistic constrained nonlinear optimization framework to optimize RED parameters. Performance Evaluation 66(2), 81-104 (2009)
9. Ruppert, D.: A Newton-Raphson version of the multivariate Robbins-Monro procedure. Annals of Statistics 13, 236-245 (1985)
10. Spall, J.C.: Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans. Auto. Cont. 37(3), 332-341 (1992)
11. Spall, J.C.: Adaptive stochastic approximation by the simultaneous perturbation method. IEEE Trans. Autom. Contr. 45, 1839-1853 (2000)
12. Spall, J.C.: Feedback and weighting mechanisms for improving Jacobian estimates in the adaptive simultaneous perturbation algorithm. IEEE Transactions on Automatic Control 54(6), 1216-1229 (2009)
13. Zhu, X., Spall, J.C.: A modified second-order SPSA optimization algorithm for finite samples. Int. J. Adapt. Control Signal Process. 16, 397-409 (2002)