检索结果-内蒙古大学图书馆

The adventures of a simple algorithm

linear ALGEBRA AND ITS APPLICATIONS 2003年 361卷 41-61页

作者： Dax, A Hydrol Serv IL-91360 Jerusalem Israel

This paper presents, analyzes, and tests a row-action method for solving the regularized linear programming problem: minimize 1/2parallel toxparallel to(2)(2) + alphac(T)x subject to Ax greater than or equal to b, where a is a given positive constant. The proposed method is based on the observation that the dual of this problem has the form: maximize b(T)y - 1/2parallel to A(T) y - alphacparallel to(2)(2) subject to y greater than or equal to 0. and if y(alpha) solves the dual then the point x(alpha) A(T)y(alpha) - alphac provides the unique solution of the primal. Maximizing the dual objective function by changing one variable at a time results in an effective row-action method which is suitable for solving large sparse problems. One aim of this paper is to clarify the convergence properties of the proposed scheme. Let Y-k denote the estimated dual solution at the end of the kth iteration, and let X-k = A(T) y(k) - alphac denote the corresponding primal estimate. It is proved that the sequence {x(k)} converges to x(alpha), while the sequence {y(k)} converges to a point y(alpha) that solves the dual. The only assumption which is needed in order to establish these claims is that the feasible region is not empty. Yet perhaps the more striking features of the algorithm are related to temporary situations in which it attempts to solve an inconsistent system. In such cases the sequence {y(k)} obeys the rule: y(k) = u(k) + kv. where {u(k)} is a fastly converging sequence and v is a fixed vector that satisfies A(T)v = 0 and b(T)v > 0. So the sequence {X-k} is almost unchanged for many iterations, The paper ends with numerical experiments that illustrate the effects of this phenomenon and the close links with Kaczmarz's SOR method. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： regularized linear programming row-action methods constrained SOR methods

来源：评论

学校读者我要写书评

暂无评论

The adventures of a simple algorithm

The adventures of a simple algorithm

引用

9th Conference of the International-linear-Algebra-Society

作者： Dax, A Hydrol Serv IL-91360 Jerusalem Israel

关键词： regularized linear programming row-action methods constrained SOR methods

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：