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CARTopt: a random search method for nonsmooth unconstrained optimization

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  • B. Robertson
  • C. Price
  • M. Reale

Abstract

A random search algorithm for unconstrained local nonsmooth optimization is described. The algorithm forms a partition on $\mathbb{R}^{n}$ using classification and regression trees (CART) from statistical pattern recognition. The CART partition defines desirable subsets where the objective function f is relatively low, based on previous sampling, from which further samples are drawn directly. Alternating between partition and sampling phases provides an effective method for nonsmooth optimization. The sequence of iterates {z k } is shown to converge to an essential local minimizer of f with probability one under mild conditions. Numerical results are presented to show that the method is effective and competitive in practice. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • B. Robertson & C. Price & M. Reale, 2013. "CARTopt: a random search method for nonsmooth unconstrained optimization," Computational Optimization and Applications, Springer, vol. 56(2), pages 291-315, October.
    • Handle: RePEc:spr:coopap:v:56:y:2013:i:2:p:291-315
    DOI: 10.1007/s10589-013-9560-9
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    Cited by:

    1. Wickramarachchi, D.C. & Robertson, B.L. & Reale, M. & Price, C.J. & Brown, J., 2016. "HHCART: An oblique decision tree," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 12-23.

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