A CARTOPT METHOD FOR BOUND-CONSTRAINED GLOBAL OPTIMIZATION

被引：6

作者：

Robertson, B. L. ^{[1
]}

Price, C. J. ^{[2
]}

Reale, M. ^{[2
]}

机构：

[1] Univ Wyoming, Dept Stat, Laramie, WY 82071 USA

[2] Univ Canterbury, Dept Math & Stat, Christchurch, New Zealand

来源：

ANZIAM JOURNAL | 2013年 / 55卷 / 02期

关键词：

CART; Halton sequence; numerical results; random search; stochastic global optimization;

D O I：

10.1017/S1446181113000412

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：109 / 128

页数：20