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Global and Finite Convergence of a Generalized Newton Method for Absolute Value Equations

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Abstract

We investigate an efficient method for solving the absolute value equation Ax−|x|=b when the interval matrix [A−I,A+I] is regular. A generalized Newton method which combines the semismooth and the smoothing Newton steps is proposed. We establish global and finite convergence of the method. Preliminary numerical results indicate that the generalized Newton method is promising.

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Authors and Affiliations

  1. Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China

    C. Zhang & Q. J. Wei

Authors
  1. C. Zhang
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  2. Q. J. Wei
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Corresponding author

Correspondence to C. Zhang.

Additional information

Communicated by O.L. Mangasarian.

This work was supported by the National Natural Science Foundation of China (70871008) and the Foundation of Beijing Jiaotong University (2008RC022).

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Zhang, C., Wei, Q.J. Global and Finite Convergence of a Generalized Newton Method for Absolute Value Equations. J Optim Theory Appl 143, 391–403 (2009). https://doi.org/10.1007/s10957-009-9557-9

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  • DOI: https://doi.org/10.1007/s10957-009-9557-9

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