10.3969/j.issn.1005-3085.2013.01.012
A New Semi-smooth Newton Method for Absolute Value Equations?
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.
absolute value equation、interval matrix、semi-smooth Newton method、global and finite convergence
O151;O221(代数、数论、组合理论)
2013-03-19(万方平台首次上网日期,不代表论文的发表时间)
共11页
101-111