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Simultaneous Perturbation Newton Algorithms for Simulation Optimization

Bhatnagar, Shalabh and Prashanth, LA (2015) Simultaneous Perturbation Newton Algorithms for Simulation Optimization. In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 164 (2). pp. 621-643.

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Official URL: http://dx.doi.org/ 10.1007/s10957-013-0507-1

Abstract

We present a new Hessian estimator based on the simultaneous perturbation procedure, that requires three system simulations regardless of the parameter dimension. We then present two Newton-based simulation optimization algorithms that incorporate this Hessian estimator. The two algorithms differ primarily in the manner in which the Hessian estimate is used. Both our algorithms do not compute the inverse Hessian explicitly, thereby saving on computational effort. While our first algorithm directly obtains the product of the inverse Hessian with the gradient of the objective, our second algorithm makes use of the Sherman-Morrison matrix inversion lemma to recursively estimate the inverse Hessian. We provide proofs of convergence for both our algorithms. Next, we consider an interesting application of our algorithms on a problem of road traffic control. Our algorithms are seen to exhibit better performance than two Newton algorithms from a recent prior work.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the SPRINGER/PLENUM PUBLISHERS, 233 SPRING ST, NEW YORK, NY 10013 USA
Keywords: Newton algorithms; Stochastic approximation; Simultaneous perturbation stochastic approximation; Three-simulation; Hessian estimate; Sherman-Morrison lemma; Application to road traffic control
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 20 Feb 2015 12:06
Last Modified: 20 Feb 2015 12:06
URI: http://eprints.iisc.ac.in/id/eprint/50841

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