Nonlinear complementarity functions for plasticity problems with frictional contact

2009 ◽  
Vol 198 (41-44) ◽  
pp. 3411-3427 ◽  
Author(s):  
Corinna Hager ◽  
B.I. Wohlmuth
Keyword(s):  
Frictional Contact ◽  
Nonlinear Complementarity ◽  
Complementarity Functions

scholarly journals A Double Nonmonotone Quasi-Newton Method for Nonlinear Complementarity Problem Based on Piecewise NCP Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhensheng Yu ◽  
Zilun Wang ◽  
Ke Su
Keyword(s):  
Global Convergence ◽  
Newton Method ◽  
Complementarity Problem ◽  
Line Search ◽  
Nonlinear Complementarity Problem ◽  
Practical Applications ◽  
Nonlinear Complementarity ◽  
Complementarity Functions ◽  
Single Solution ◽  
Quasi Newton

In this paper, a double nonmonotone quasi-Newton method is proposed for the nonlinear complementarity problem. By using 3-1 piecewise and 4-1 piecewise nonlinear complementarity functions, the nonlinear complementarity problem is reformulated into a smooth equation. By a double nonmonotone line search, a smooth Broyden-like algorithm is proposed, where a single solution of a smooth equation at each iteration is required with the reduction in the scale of the calculation. Under suitable conditions, the global convergence of the algorithm is proved, and numerical results with some practical applications are given to show the efficiency of the algorithm.

scholarly journals A local Jacobian smoothing method for solving Nonlinear Complementarity Problems

2020 ◽  
Vol 25 (1) ◽  
pp. 149-174
Author(s):  
Favian E Arenas ◽  
Héctor Jairo Martínez ◽  
Rosana Pérez
Keyword(s):  
Complementarity Problem ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Smoothing Method ◽  
System Of Equations ◽  
Nonlinear Complementarity ◽  
Complementarity Functions ◽  
Type Algorithm ◽  
Numerical Performance ◽  
Generalized Newton

In this paper, we present a smoothing of a family of nonlinear complementarity functions and use its properties in combination with the smooth Jacobian strategy to present a new generalized Newton-type algorithm to solve a nonsmooth system of equations equivalent to the Nonlinear Complementarity Problem. In addition, we prove that the algorithm converges locally and q-quadratically, and analyze its numerical performance.

scholarly journals Least Change Secant Update Methods for Nonlinear Complementarity Problem

2015 ◽  
Vol 11 (21) ◽  
pp. 11-21 ◽  
Author(s):  
Favián Arenas A ◽  
Héctor J Martínez ◽  
Rosana Pérez M
Keyword(s):  
Superlinear Convergence ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Nonlinear Complementarity ◽  
Complementarity Functions ◽  
The One ◽  
Local And Superlinear Convergence ◽  
Parametric Class

In this work, we introduce a family of Least Change Secant Update Methods for solving Nonlinear Complementarity Problems based on its reformulation as a nonsmooth system using the one-parametric class of nonlinear complementarity functions introduced by Kanzow and Kleinmichel. We prove local and superlinear convergence for the algorithms. Some numerical experiments show a good performance of this algorithm.

Sign in / Sign up

Export Citation Format

Share Document