Absolute value equation solution via concave minimization期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Absolute value equation solution via concave minimization

Authors:	O L Mangasarian

Institution:	(1) Computer Sciences Department, University of Wisconsin, Madison, WI 53706, USA;(2) Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, USA

Abstract:	The NP-hard absolute value equation (AVE) Ax − \|x\| = b where $A\in R^{n\times n}$ and $b\in R^n$ is solved by a succession of linear programs. The linear programs arise from a reformulation of the AVE as the minimization of a piecewise-linear concave function on a polyhedral set and solving the latter by successive linearization. A simple MATLAB implementation of the successive linearization algorithm solved 100 consecutively generated 1,000-dimensional random instances of the AVE with only five violated equations out of a total of 100,000 equations.

Keywords:	Absolute value equation Concave minimization Successive linear programming
本文献已被 SpringerLink 等数据库收录！