Abstract
Gaussian SF estimates of the Hessian are derived by taking the convolution of the Hessian of the objective function with a multi-variate Gaussian density functional. Through an integration-by-parts argument applied twice, the same is seen to be the convolution of the function itself with a scaled multi-variate Gaussian density. This results in a one-simulation estimate of the Hessian. The same simulation also helps in obtaining a one-simulation gradient estimate (see ChapterĀ 6). Thus, one obtains a one-simulation Newton-based SF algorithm. A two-simulation estimate of the Hessian is also derived that incorporates the same two simulations as for the two-simulation gradient estimate, also derived in ChapterĀ 6. This results in a two-simulation Newton SF algorithm. We limit the discussion in this chapter to Gaussian-based SF estimates only.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bhatnagar, S.: Adaptive multivariate three-timescale stochastic approximation algorithms for simulation based optimization. ACM Transactions on Modeling and Computer SimulationĀ 15(1), 74ā107 (2005)
Bhatnagar, S.: Adaptive Newton-based smoothed functional algorithms for simulation optimization. ACM Transactions on Modeling and Computer SimulationĀ 18(1), 2:1ā2:35 (2007)
Bhatnagar, S., Mishra, V., Hemachandra, N.: Stochastic algorithms for discrete parameter simulation optimization. IEEE Transactions on Automation Science and EngineeringĀ 9(4), 780ā793 (2011)
Kushner, H.J., Clark, D.S.: Stochastic Approximation Methods for Constrained and Unconstrained Systems. Springer, New York (1978)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
Ā© 2013 Springer-Verlag London
About this chapter
Cite this chapter
Bhatnagar, S., Prasad, H., Prashanth, L. (2013). Newton-Based Smoothed Functional Algorithms. In: Stochastic Recursive Algorithms for Optimization. Lecture Notes in Control and Information Sciences, vol 434. Springer, London. https://doi.org/10.1007/978-1-4471-4285-0_8
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4285-0_8
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4284-3
Online ISBN: 978-1-4471-4285-0
eBook Packages: EngineeringEngineering (R0)