CARTopt: a random search method for nonsmooth unconstrained optimization

Authors:
B. L. Robertson;C. J. Price;M. Reale
Affiliations:
Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand;Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand;Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand
Venue:
Computational Optimization and Applications
Year:
2013

Citing 15
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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 {zk} 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.