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Random-Direction Optimization Algorithms with Applications to Threshold Controls

Author

Listed:
  • G. Yin

    (Wayne State University)

  • Q. Zhang

    (University of Georgia)

  • H. M. Yan

    (Chinese University of Hong Kong)

  • E. K. Boukas

    (École Polytechnique de Montréal)

Abstract

This work develops a class of stochastic optimization algorithms. It aims to provide numerical procedures for solving threshold-type optimal control problems. The main motivation stems from applications involving optimal or suboptimal hedging policies, for example, production planning of manufacturing systems including random demand and stochastic machine capacity. The proposed algorithm is a constrained stochastic approximation procedure that uses random-direction finite-difference gradient estimates. Under fairly general conditions, the convergence of the algorithm is established and the rate of convergence is also derived. A numerical example is reported to demonstrate the performance of the algorithm.

Suggested Citation

  • G. Yin & Q. Zhang & H. M. Yan & E. K. Boukas, 2001. "Random-Direction Optimization Algorithms with Applications to Threshold Controls," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 211-233, July.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:1:d:10.1023_a:1017555931930
    DOI: 10.1023/A:1017555931930
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    References listed on IDEAS

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    1. Houmin Yan & Xun Yu Zhou & G. Yin, 1999. "Approximating an Optimal Production Policy in a Continuous Flow Line: Recurrence and Asymptotic Properties," Operations Research, INFORMS, vol. 47(4), pages 535-549, August.
    2. T. Bielecki & P. R. Kumar, 1988. "Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems," Operations Research, INFORMS, vol. 36(4), pages 532-541, August.
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