Combined interior-point method and semismooth Newton method for frictionless contact problems

2009 ◽  
Vol 81 (6) ◽  
pp. 701-727 ◽  
Author(s):  
Tomoshi Miyamura ◽  
Yoshihiro Kanno ◽  
Makoto Ohsaki
Keyword(s):  
Newton Method ◽  
Interior Point ◽  
Interior Point Method ◽  
Contact Problems ◽  
Point Method ◽  
Semismooth Newton Method ◽  
Frictionless Contact ◽  
Semismooth Newton

scholarly journals A new semismooth Newton method for solving finite-dimensional quasi-variational inequalities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shui-Lian Xie ◽  
Zhe Sun ◽  
Hong-Ru Xu
Keyword(s):  
Variational Inequalities ◽  
Newton Method ◽  
Interior Point Method ◽  
Inequality Constraints ◽  
Semismooth Newton Method ◽  
Finite Dimensional ◽  
Math Program ◽  
Semismooth Newton ◽  
Equality And Inequality Constraints ◽  
Quasi Variational Inequality

AbstractIn this paper, we consider the numerical method for solving finite-dimensional quasi-variational inequalities with both equality and inequality constraints. Firstly, we present a semismooth equation reformulation to the KKT system of a finite-dimensional quasi-variational inequality. Then we propose a semismooth Newton method to solve the equations and establish its global convergence. Finally, we report some numerical results to show the efficiency of the proposed method. Our method can obtain the solution to some problems that cannot be solved by the method proposed in (Facchinei et al. in Comput. Optim. Appl. 62:85–109, 2015). Besides, our method outperforms than the interior point method proposed in (Facchinei et al. in Math. Program. 144:369–412, 2014).

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