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  • Probability in the Engineering and Informational Sciences, Volume 12, Issue 4
  • October 1998, pp. 519-531

A two Timescale Stochastic Approximation Scheme for Simulation-Based Parametric Optimization

  • Shalabh Bhatnagar (a1) and Vivek S. Borkar (a2)
  • DOI: http://dx.doi.org/10.1017/S0269964800005362
  • Published online: 01 July 2009
Abstract

A two timescale stochastic approximation scheme which uses coupled iterations is used for simulation-based parametric optimization as an alternative to traditional “infinitesimal perturbation analysis” schemes. It avoids the aggregation of data present in many other schemes. Its convergence is analyzed, and a queueing example is presented.

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3.V.S. Borkar (1997). Stochastic approximation with two time scales. Systems and Control Letters 29: 291294.

4.E.K.P. Chong & R.J. Ramadge (1994). Stochastic optimization of regenerative systems using infinitesimal perturbation analysis. IEEE Transactions on Automatic Control 39(7): 14001410.

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7.H.J. Kushner & D.S. Clark (1978). Stochastic approximation methods for constrained and unconstrained systems. New York: Springer Verlag.

8.P. L'Ecuyer & P.W. Glynn (1994). Stochastic optimization by simulation: Convergence proofs for the GI/G/I queue in steady state. Management Science 40(11): 15621578.

10.R. Rubinstein (1981). Simulation and the Monte Carlo Method. New York: John Wiley.

11.A. Ruszczynski & W. Syski (1983). Stochastic approximation method with gradient averaging for unconstrained problems. IEEE Transactions on Automatic Control AC-28(12): 10971105.

12.J.C. Spall (1992). Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Transactions on Automatic Control 37(3): 332341.

13.R. Suri & M.A. Zazanis (1988). Perturbation analysis gives strongly consistent estimates for the M/G/1 queue. Management Science 34(1): 3964.

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