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A CARTOPT METHOD FOR BOUND-CONSTRAINED GLOBAL OPTIMIZATION

Published online by Cambridge University Press:  18 March 2014

B. L. ROBERTSON ,
C. J. PRICE  and
M. REALE
B. L. ROBERTSON*
Affiliation:
Department of Statistics, University of Wyoming, Laramie, Wyoming, USA
C. J. PRICE
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand email chrisj.price@canterbury.ac.nz email marco.reale@canterbury.ac.nz
M. REALE
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand email chrisj.price@canterbury.ac.nz email marco.reale@canterbury.ac.nz
*
✉brober25@uwyo.edu
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Abstract

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A stochastic algorithm for bound-constrained global optimization is described. The method can be applied to objective functions that are nonsmooth or even discontinuous. The algorithm forms a partition on the search region using classification and regression trees (CART), which defines a region where the objective function is relatively low. Further points are drawn directly from the low region before a new partition is formed. Alternating between partition and sampling phases provides an effective method for nonsmooth global optimization. The sequence of iterates generated by the algorithm is shown to converge to an essential global minimizer with probability one under mild conditions. Nonprobabilistic results are also given when random sampling is replaced with points taken from the Halton sequence. Numerical results are presented for both smooth and nonsmooth problems and show that the method is effective and competitive in practice.

Keywords

CARTHalton sequencenumerical resultsrandom searchstochastic global optimization

MSC classification

Secondary: 90C26: Nonconvex programming, global optimization
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 2 , October 2013 , pp. 109 - 128
Copyright
Copyright © 2014 Australian Mathematical Society 

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