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A generalized Newton method for absolute value equations

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Abstract

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 × 1,000 nonsymmetric positive definite matrices were also solved to the same accuracy in less than 29 s each.

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Correspondence to O. L. Mangasarian.

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Mangasarian, O.L. A generalized Newton method for absolute value equations. Optim Lett 3, 101–108 (2009). https://doi.org/10.1007/s11590-008-0094-5

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  • DOI: https://doi.org/10.1007/s11590-008-0094-5

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