A globally and quadratically convergent method for absolute value equations

Authors:
Louis Caccetta;Biao Qu;Guanglu Zhou
Affiliations:
Western Australian Centre of Excellence in Industrial Optimisation (WACEIO), Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia 6845;Institute of Operations Research, Qufu Normal University, Rizhao, P.R. China 276826;Western Australian Centre of Excellence in Industrial Optimisation (WACEIO), Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia 6845
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

We investigate the NP-hard absolute value equation (AVE) Ax驴|x|=b, where A is an arbitrary n脳n real matrix. In this paper, we propose a smoothing Newton method for the AVE. When the singular values of A exceed 1, we show that this proposed method is globally convergent and the convergence rate is quadratic. Preliminary numerical results show that this method is promising.