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Volume 2, Issue 2
Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities

Liu Yang, Yanping Chen & Xiaojiao Tong

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 224-236.

Published online: 2009-02

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  • Abstract

In this paper, we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities. By using the so-called max function, we transfer the inequalities into a system of semismooth equalities. Then a smoothing Newton-like method is proposed for solving the reformulated system, which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.

  • Keywords

Nonlinear systems of equalities and inequalities, semismooth function, smoothing Newton method, global convergence, local quadratic convergence.

  • AMS Subject Headings

65K05, 90C30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-224, author = {}, title = {Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {2}, pages = {224--236}, abstract = {

In this paper, we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities. By using the so-called max function, we transfer the inequalities into a system of semismooth equalities. Then a smoothing Newton-like method is proposed for solving the reformulated system, which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6023.html} }
TY - JOUR T1 - Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 224 EP - 236 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6023.html KW - Nonlinear systems of equalities and inequalities, semismooth function, smoothing Newton method, global convergence, local quadratic convergence. AB -

In this paper, we present a smoothing Newton-like method for solving nonlinear systems of equalities and inequalities. By using the so-called max function, we transfer the inequalities into a system of semismooth equalities. Then a smoothing Newton-like method is proposed for solving the reformulated system, which only needs to solve one system of linear equations and to perform one line search at each iteration. The global and local quadratic convergence are studied under appropriate assumptions. Numerical examples show that the new approach is effective.

Liu Yang, Yanping Chen & Xiaojiao Tong. (2020). Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities. Numerical Mathematics: Theory, Methods and Applications. 2 (2). 224-236. doi:
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