Optimization Letters

, Volume 3, Issue 1, pp 101–108

A generalized Newton method for absolute value equations

Original Paper

DOI: 10.1007/s11590-008-0094-5

Cite this article as:
Mangasarian, O.L. Optim Lett (2009) 3: 101. doi:10.1007/s11590-008-0094-5


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.


Absolute value equationGeneralized NewtonLinear complementarity problems

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsUniversity of California at San DiegoLa JollaUSA