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Smoothing Newton-Like Method for the Solution of Nonlinear Systems of Equalities and Inequalities |
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| Authors: | Liu Yang Yanping Chen Xiaojiao Tong |
| Institution: | 1. School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,Hunan,China. 2. School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China. 3. School of Mathematics and Computational Science,Changsha University of Science and Technology,Changsha 410076,Hunan,China. |
| Abstract: | In this paper, we present a smoothing Newton-like method for solving non-linear 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 |
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