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The robust constant and its applications in random global search for unconstrained global optimization

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  • Zheng Peng
  • Donghua Wu
  • Wenxing Zhu

Abstract

Robust analysis is important for designing and analyzing algorithms for global optimization. In this paper, we introduce a new concept, robust constant, to quantitatively characterize the robustness of measurable sets and functions. The new concept is consistent to the theoretical robustness presented in literatures. This paper shows that, from the respects of convergence theory and numerical computational cost, robust constant is valuable significantly for analyzing random global search methods for unconstrained global optimization. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Zheng Peng & Donghua Wu & Wenxing Zhu, 2016. "The robust constant and its applications in random global search for unconstrained global optimization," Journal of Global Optimization, Springer, vol. 64(3), pages 469-482, March.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:3:p:469-482
    DOI: 10.1007/s10898-014-0256-1
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    References listed on IDEAS

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    1. Reuven Rubinstein, 1999. "The Cross-Entropy Method for Combinatorial and Continuous Optimization," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 127-190, September.
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    3. Samuel H. Brooks, 1958. "A Discussion of Random Methods for Seeking Maxima," Operations Research, INFORMS, vol. 6(2), pages 244-251, April.
    4. Dirk P. Kroese & Sergey Porotsky & Reuven Y. Rubinstein, 2006. "The Cross-Entropy Method for Continuous Multi-Extremal Optimization," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 383-407, September.
    5. D. Bulger & W. P. Baritompa & G. R. Wood, 2003. "Implementing Pure Adaptive Search with Grover's Quantum Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 517-529, March.
    6. Zheng Peng & Donghua Wu & Quan Zheng, 2013. "A Level-Value Estimation Method and Stochastic Implementation for Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 493-523, February.
    7. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
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    Cited by:

    1. Dawid Tarłowski, 2017. "On the convergence rate issues of general Markov search for global minimum," Journal of Global Optimization, Springer, vol. 69(4), pages 869-888, December.

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