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MSO: a framework for bound-constrained black-box global optimization algorithms

Author

Listed:
  • Abdullah Al-Dujaili

    (Nanyang Technological University)

  • S. Suresh

    (Nanyang Technological University)

  • N. Sundararajan

    (Nanyang Technological University)

Abstract

This paper addresses a class of algorithms for solving bound-constrained black-box global optimization problems. These algorithms partition the objective function domain over multiple scales in search for the global optimum. For such algorithms, we provide a generic procedure and refer to as multi-scale optimization (MSO). Furthermore, we propose a theoretical methodology to study the convergence of MSO algorithms based on three basic assumptions: (a) local Hölder continuity of the objective function f, (b) partitions boundedness, and (c) partitions sphericity. Moreover, the worst-case finite-time performance and convergence rate of several leading MSO algorithms, namely, Lipschitzian optimization methods, multi-level coordinate search, dividing rectangles, and optimistic optimization methods have been presented.

Suggested Citation

  • Abdullah Al-Dujaili & S. Suresh & N. Sundararajan, 2016. "MSO: a framework for bound-constrained black-box global optimization algorithms," Journal of Global Optimization, Springer, vol. 66(4), pages 811-845, December.
    • Handle: RePEc:spr:jglopt:v:66:y:2016:i:4:d:10.1007_s10898-016-0441-5
    DOI: 10.1007/s10898-016-0441-5
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    References listed on IDEAS

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    1. Jaroslav Fowkes & Nicholas Gould & Chris Farmer, 2013. "A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions," Journal of Global Optimization, Springer, vol. 56(4), pages 1791-1815, August.
    2. Qunfeng Liu & Wanyou Cheng, 2014. "A modified DIRECT algorithm with bilevel partition," Journal of Global Optimization, Springer, vol. 60(3), pages 483-499, November.
    3. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
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    1. Abdullah Al-Dujaili & S. Suresh, 2019. "Revisiting norm optimization for multi-objective black-box problems: a finite-time analysis," Journal of Global Optimization, Springer, vol. 73(3), pages 659-673, March.

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