THE BISECTION METHOD IN HIGHER DIMENSIONS

被引：55

作者：

WOOD, GR

机构：

[1] Mathematics Department, University of Canterbury, Christchurch

来源：

MATHEMATICAL PROGRAMMING | 1992年 / 55卷 / 03期

关键词：

BISECTION; SIMPLEX; GLOBAL OPTIMIZATION; LINEAR CONVERGENCE; ZONOTOPE; TILING;

D O I：

10.1007/BF01581205

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Is the familiar bisection method part of some larger scheme? The aim of this paper is to present a natural and useful generalisation of the bisection method to higher dimensions. The algorithm preserves the salient features of the bisection method: it is simple, convergence is assured and linear, and it proceeds via a sequence of brackets whose infinite intersection is the set of points desired. Brackets are unions of similar simplexes. An immediate application is to the global minimisation of a Lipschitz continuous function defined on a compact subset of Euclidean space.

引用

页码：319 / 337

页数：19

共 10 条

[1] ITERATIVE METHODS FOR THE LOCALIZATION OF THE GLOBAL MAXIMUM [J].