A New Semi-smooth Newton Method for Absolute Value Equations?

• 作者: LIU Chang-he LIU Hong-wei ZHU Jian-guang
• 来源期刊: 工程数学学报
• 学科: 数学
• 关键词: absolute value equation interval matrix semi-smooth Newton method global and finite convergence
• 年，卷（期）: 2013,（1）
• 页码范围: 101-111
• 分类号: O151|O221
• 字数: 883字
• 语种: 中文
• DOI: 10.3969/j.issn.1005-3085.2013.01.012

摘要

Absolute value equation (AVE):Ax?|x|=b, where A is an n×n real matrix, arising in solving systems of interval linear equations. Linear complementarity problem, which subsumes many mathematical programming problems, can be formulated as an AVE. A semi-smooth Newton algorithm is proposed for solving the AVE. In the algorithm, two non-smooth equation reformulations are used. They are constructed based on the min- and FB-function, respectively. At each iteration, however, only one system of linear equations needs to be solved. The algorithm is globally and finitely convergent, under the condition that the interval matrix [A?I, A+I] is regular. The proposed algorithm was tested on 100 consecutively generated random instances of the AVE with n =1000. All of these test problems are well solved, with accuracy of 10?6.