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Zbl 1154.90599
Mangasarian, O.L.
A generalized Newton method for absolute value equations. (English)
[J] Optim. Lett. 3, No. 1, 101-108 (2009). ISSN 1862-4472; ISSN 1862-4480/e

Summary: A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) $Ax - |x| = b$ when the singular values of $A$ exceed 1. A simple MATLAB implementation of the method solved 100 randomly generated 1,000-dimensional AVEs to an accuracy of $10^{-6}$ in less than 10 s each. Similarly, AVEs corresponding to 100 randomly generated linear complementarity problems with $1,000 \times 1,000$ nonsymmetric positive definite matrices were also solved to the same accuracy in less than 29 s each.

MSC 2000:: *90C33 Complementarity problems
90C53 Methods of quasi-Newton type

Keywords: absolute value equation; generalized Newton; linear complementarity problems

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Zentralblatt MATH Berlin [Germany]