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CARTopt: a random search method for nonsmooth unconstrained optimization. (English) Zbl 1312.90065
Summary: 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.

MSC:
 90C26 Nonconvex programming, global optimization
Software:
CARTopt; Matlab; minpack
Full Text:
References:
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