Quasi-Newton smoothed functional algorithms for unconstrained and constrained simulation optimization

Lakshmanan, K and Bhatnagar, Shalabh (2017) Quasi-Newton smoothed functional algorithms for unconstrained and constrained simulation optimization. In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 66 (3). pp. 533-556.

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Abstract

We propose a multi-time scale quasi-Newton based smoothed functional (QN-SF) algorithm for stochastic optimization both with and without inequality constraints. The algorithm combines the smoothed functional (SF) scheme for estimating the gradient with the quasi-Newton method to solve the optimization problem. Newton algorithms typically update the Hessian at each instant and subsequently (a) project them to the space of positive definite and symmetric matrices, and (b) invert the projected Hessian. The latter operation is computationally expensive. In order to save computational effort, we propose in this paper a quasi-Newton SF (QN-SF) algorithm based on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) update rule. In Bhatnagar (ACM TModel Comput S. 18(1): 27-62, 2007), a Jacobi variant of Newton SF (JN-SF) was proposed and implemented to save computational effort. We compare our QN-SF algorithm with gradient SF (G-SF) and JN-SF algorithms on two different problems - first on a simple stochastic function minimization problem and the other on a problem of optimal routing in a queueing network. We observe from the experiments that the QN-SF algorithm performs significantly better than both G-SF and JN-SF algorithms on both the problem settings. Next we extend the QN-SF algorithm to the case of constrained optimization. In this case too, the QN-SF algorithm performs much better than the JN-SF algorithm. Finally we present the proof of convergence for the QN-SF algorithm in both unconstrained and constrained settings.

Item Type:	Journal Article
Publication:	COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
Additional Information:	Copy right for this article belongs to the SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	26 Apr 2017 07:23
Last Modified:	26 Apr 2017 07:23
URI:	http://eprints.iisc.ac.in/id/eprint/56637

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