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Cumulative weighting optimization

Author

Listed:
  • Kun Lin

    (University of Maryland, College Park)

  • Steven I. Marcus

    (University of Maryland, College Park)

Abstract

Global optimization problems with limited structure (e.g., convexity or differentiability of the objective function) can arise in many fields. One approach to solving these problems is by modeling the evolution of a probability density function over the solution space, similar to the Fokker–Planck equation for diffusions, such that at each time instant, additional weight is given to better solutions. We propose an addition to the class of model-based methods, cumulative weighting optimization (CWO), whose general version can be proven convergent to an optimal solution and stable under disturbances (e.g., floating point inaccuracy). These properties encourage us to design a class of CWO algorithms for solving global optimization problems. Beyond the general convergence and stability analysis, we prove that with some additional assumptions the Monte Carlo version of the CWO algorithm is also convergent and stable. Interestingly, the well known cross-entropy method is a CWO algorithm.

Suggested Citation

  • Kun Lin & Steven I. Marcus, 2016. "Cumulative weighting optimization," Journal of Global Optimization, Springer, vol. 65(3), pages 487-512, July.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:3:d:10.1007_s10898-015-0374-4
    DOI: 10.1007/s10898-015-0374-4
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    References listed on IDEAS

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    1. Jiaqiao Hu & Michael C. Fu & Steven I. Marcus, 2007. "A Model Reference Adaptive Search Method for Global Optimization," Operations Research, INFORMS, vol. 55(3), pages 549-568, June.
    2. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    3. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    4. Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009. "Brown-von Neumann-Nash dynamics: The continuous strategy case," Games and Economic Behavior, Elsevier, vol. 65(2), pages 406-429, March.
    5. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    6. Mohammed Abdellaoui & Olivier l’Haridon & Horst Zank, 2009. "Separating Curvature and Elevation: A Parametric Weighting Function," Economics Discussion Paper Series 0901, Economics, The University of Manchester.
    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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