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Volume 43, Issue 2
A Non-Monotone Smoothing Newton Algorithm for Solving the System of Generalized Absolute Value Equations

Cairong Chen, Dongmei Yu, Deren Han & Changfeng Ma

DOI: 10.4208/jcm.2211-m2022-0083

J. Comp. Math., 43 (2025), pp. 438-460.

Published online: 2024-11

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  • Abstract

The system of generalized absolute value equations (GAVE) has attracted more and more attention in the optimization community. In this paper, by introducing a smoothing function, we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE. We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE. Numerical results are given to demonstrate the viability and efficiency of the approach.

  • Keywords

Generalized absolute value equations, Smoothing function, Smoothing Newton algorithm, Non-monotone line search, Global and local quadratic convergence.

  • AMS Subject Headings

65F10, 65H10, 90C30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-43-438, author = {Chen , CairongYu , DongmeiHan , Deren and Ma , Changfeng}, title = {A Non-Monotone Smoothing Newton Algorithm for Solving the System of Generalized Absolute Value Equations}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {43}, number = {2}, pages = {438--460}, abstract = {

The system of generalized absolute value equations (GAVE) has attracted more and more attention in the optimization community. In this paper, by introducing a smoothing function, we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE. We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE. Numerical results are given to demonstrate the viability and efficiency of the approach.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2211-m2022-0083}, url = {http://global-sci.org/intro/article_detail/jcm/23545.html} }
TY - JOUR T1 - A Non-Monotone Smoothing Newton Algorithm for Solving the System of Generalized Absolute Value Equations AU - Chen , Cairong AU - Yu , Dongmei AU - Han , Deren AU - Ma , Changfeng JO - Journal of Computational Mathematics VL - 2 SP - 438 EP - 460 PY - 2024 DA - 2024/11 SN - 43 DO - http://doi.org/10.4208/jcm.2211-m2022-0083 UR - https://global-sci.org/intro/article_detail/jcm/23545.html KW - Generalized absolute value equations, Smoothing function, Smoothing Newton algorithm, Non-monotone line search, Global and local quadratic convergence. AB -

The system of generalized absolute value equations (GAVE) has attracted more and more attention in the optimization community. In this paper, by introducing a smoothing function, we develop a smoothing Newton algorithm with non-monotone line search to solve the GAVE. We show that the non-monotone algorithm is globally and locally quadratically convergent under a weaker assumption than those given in most existing algorithms for solving the GAVE. Numerical results are given to demonstrate the viability and efficiency of the approach.

Chen , CairongYu , DongmeiHan , Deren and Ma , Changfeng. (2024). A Non-Monotone Smoothing Newton Algorithm for Solving the System of Generalized Absolute Value Equations. Journal of Computational Mathematics. 43 (2). 438-460. doi:10.4208/jcm.2211-m2022-0083
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