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Random-Direction Optimization Algorithms with Applications to Threshold Controls

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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.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, Michigan

    G. Yin (Professor)

  2. Department of Mathematics, University of Georgia, Athens, Georgia

    Q. Zhang (Associate Professor)

  3. Department of Systems Engineering and Engineering Management, Chinese University of Hong Kong, Shatin, Hong Kong

    H. M. Yan (Associate Professor)

  4. Mechanical Engineering Department, École Polytechnique de Montréal, Montréal, Québec, Canada

    E. K. Boukas (Professor)

Authors
  1. G. Yin
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  2. Q. Zhang
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  3. H. M. Yan
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  4. E. K. Boukas
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Yin, G., Zhang, Q., Yan, H.M. et al. Random-Direction Optimization Algorithms with Applications to Threshold Controls. Journal of Optimization Theory and Applications 110, 211–233 (2001). https://doi.org/10.1023/A:1017555931930

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