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Statistical Inferences for Termination of Markov Type Random Search Algorithms

Author

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  • V. Bartkutė

    (Institute of Mathematics and Informatics)

  • L. Sakalauskas

    (Institute of Mathematics and Informatics)

Abstract

In this paper, we consider the application of order statistics to establish the optimality in stochastic and heuristic optimization algorithms. A method for estimating the minimum value with an associated confidence interval is developed using the formalism of the theory of order statistics for i.i.d. variables; we examine it by computer simulation. We build a method for the estimation of confidence intervals of the minimum value using order statistics, implemented for optimality testing and stopping in Markov type random search algorithms. The efficiency of this approach is discussed, using the results of application to stochastic approximation and simulated annealing.

Suggested Citation

  • V. Bartkutė & L. Sakalauskas, 2009. "Statistical Inferences for Termination of Markov Type Random Search Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 475-493, June.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:3:d:10.1007_s10957-008-9502-3
    DOI: 10.1007/s10957-008-9502-3
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    References listed on IDEAS

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    1. Chen, Hung & Huang, Mong-Na Lo & Huang, Wen-Jang, 1996. "Estimation of the Location of the Maximum of a Regression Function Using Extreme Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 191-214, May.
    2. Bartkute, Vaida & Sakalauskas, Leonidas, 2007. "Simultaneous perturbation stochastic approximation of nonsmooth functions," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1174-1188, September.
    3. R. L. Yang, 2000. "Convergence of the Simulated Annealing Algorithm for Continuous Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 691-716, March.
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    Cited by:

    1. Corominas, Albert, 2023. "On deciding when to stop metaheuristics: Properties, rules and termination conditions," Operations Research Perspectives, Elsevier, vol. 10(C).

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