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A globally and quadratically convergent method for absolute value equations

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Abstract

We investigate the NP-hard absolute value equation (AVE) Ax−|x|=b, where A is an arbitrary n×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.

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Authors and Affiliations

  1. Western Australian Centre of Excellence in Industrial Optimisation (WACEIO), Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia

    Louis Caccetta & Guanglu Zhou

  2. Institute of Operations Research, Qufu Normal University, Rizhao, 276826, Shandong, P.R. China

    Biao Qu

Authors
  1. Louis Caccetta
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  2. Biao Qu
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  3. Guanglu Zhou
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Correspondence to Guanglu Zhou.

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Caccetta, L., Qu, B. & Zhou, G. A globally and quadratically convergent method for absolute value equations. Comput Optim Appl 48, 45–58 (2011). https://doi.org/10.1007/s10589-009-9242-9

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  • DOI: https://doi.org/10.1007/s10589-009-9242-9

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