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On Choosing Parameters in Retrospective-Approximation Algorithms for Stochastic Root Finding and Simulation Optimization

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  • Raghu Pasupathy

    (Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia 24061)

Abstract

The stochastic root-finding problem is that of finding a zero of a vector-valued function known only through a stochastic simulation. The simulation-optimization problem is that of locating a real-valued function's minimum, again with only a stochastic simulation that generates function estimates. Retrospective approximation (RA) is a sample-path technique for solving such problems, where the solution to the underlying problem is approached via solutions to a sequence of approximate deterministic problems, each of which is generated using a specified sample size, and solved to a specified error tolerance. Our primary focus, in this paper, is providing guidance on choosing the sequence of sample sizes and error tolerances in RA algorithms. We first present an overview of the conditions that guarantee the correct convergence of RA's iterates. Then we characterize a class of error-tolerance and sample-size sequences that are superior to others in a certain precisely defined sense. We also identify and recommend members of this class and provide a numerical example illustrating the key results.

Suggested Citation

  • Raghu Pasupathy, 2010. "On Choosing Parameters in Retrospective-Approximation Algorithms for Stochastic Root Finding and Simulation Optimization," Operations Research, INFORMS, vol. 58(4-part-1), pages 889-901, August.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:4-part-1:p:889-901
    DOI: 10.1287/opre.1090.0773
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    References listed on IDEAS

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    Cited by:

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    6. Honggang Wang, 2017. "Subspace dynamic‐simplex linear interpolation search for mixed‐integer black‐box optimization problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 305-322, June.
    7. Stefania Bellavia & Nataša Krejić & Benedetta Morini, 2020. "Inexact restoration with subsampled trust-region methods for finite-sum minimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 701-736, July.
    8. Bismark Singh & David P. Morton & Surya Santoso, 2018. "An adaptive model with joint chance constraints for a hybrid wind-conventional generator system," Computational Management Science, Springer, vol. 15(3), pages 563-582, October.
    9. Devang Sinha & Siddhartha P. Chakrabarty, 2024. "Multilevel Monte Carlo in Sample Average Approximation: Convergence, Complexity and Application," Papers 2407.18504, arXiv.org.
    10. J. O. Royset & E. Y. Pee, 2012. "Rate of Convergence Analysis of Discretization and Smoothing Algorithms for Semiinfinite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 855-882, December.
    11. Kyle Cooper & Susan R. Hunter & Kalyani Nagaraj, 2020. "Biobjective Simulation Optimization on Integer Lattices Using the Epsilon-Constraint Method in a Retrospective Approximation Framework," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1080-1100, October.
    12. Hu, Shaolong & Dong, Zhijie Sasha & Dai, Rui, 2024. "A machine learning based sample average approximation for supplier selection with option contract in humanitarian relief," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 186(C).
    13. Emelogu, Adindu & Chowdhury, Sudipta & Marufuzzaman, Mohammad & Bian, Linkan & Eksioglu, Burak, 2016. "An enhanced sample average approximation method for stochastic optimization," International Journal of Production Economics, Elsevier, vol. 182(C), pages 230-252.
    14. Hu, Shaolong & Hu, Qingmi & Tao, Sha & Dong, Zhijie Sasha, 2023. "A multi-stage stochastic programming approach for pre-positioning of relief supplies considering returns," Socio-Economic Planning Sciences, Elsevier, vol. 88(C).
    15. Wang, Honggang, 2012. "Retrospective optimization of mixed-integer stochastic systems using dynamic simplex linear interpolation," European Journal of Operational Research, Elsevier, vol. 217(1), pages 141-148.
    16. Nataša Krejić & Nataša Krklec Jerinkić, 2019. "Spectral projected gradient method for stochastic optimization," Journal of Global Optimization, Springer, vol. 73(1), pages 59-81, January.
    17. Xiang He & Xiqun (Michael) Chen & Chenfeng Xiong & Zheng Zhu & Lei Zhang, 2017. "Optimal Time-Varying Pricing for Toll Roads Under Multiple Objectives: A Simulation-Based Optimization Approach," Transportation Science, INFORMS, vol. 51(2), pages 412-426, May.
    18. Johannes O. Royset & Roberto Szechtman, 2013. "Optimal Budget Allocation for Sample Average Approximation," Operations Research, INFORMS, vol. 61(3), pages 762-776, June.

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