Newton iterations in implicit time-stepping scheme for differential linear complementarity systems
type: Item
instance of: scholarly article
title: Newton iterations in implicit time-stepping scheme for differential linear complementarity systems
zbMATH Open document ID: 1276.90066
author: Shuhuang Xiang
author: Xiaojun Chen
published in: Mathematical Programming. Series A. Series B
publication date: 2013-05-06T00:00:00Z
review text: The authors consider the following ordinary differential linear complementarity sytem: \[ \begin{gathered} dx/dt= Ax(t)+ By(t)+ f(t),\\ y(t)^T(Nx(t)+ g(t)+ My(t)= 0,\quad y(t)\geq 0,\\ x(0)= x_0,\quad t\in [0,T],\end{gathered} \] where \(A\in\mathbb{R}^{m\times m}\), \(B\in \mathbb{R}^{m\times n}\), \(N\in\mathbb{R}^{n\times m}\), \(M\in\mathbb{R}^{n\times n}\) are given matrices and \(f: \mathbb{R}\to\mathbb{R}^m\), \(g: \mathbb{R}\to \mathbb{R}^n\) are two given Lipschitz continuous functions. The authors propose a time-stepping method for solving the system. The method uses a finite-difference formula to approximate the derivative \(dx(t)/dt\). A Lipschitz continuous solution function \(y(.)\) is found. A simple formula to compute an element in the Clarke generalized Jacobian of the solution function is derived. A sharp and computable Lipschitz constant of \(y(.)\) is prescribed. A superlinear convergence rate of the proposed time-stepping scheme for a class of the given differential linear complementarity system is proved.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L60
zbMATH DE Number: 6160896
zbMATH Keywords: differential linear complementarity problem
zbMATH Keywords: least-norm solution
zbMATH Keywords: least-element solution
zbMATH Keywords: nondegenerate matrix
zbMATH Keywords: \(Z\)-matrix
zbMATH Keywords: generalized Newton method
MaRDI profile type: Publication
full work available at URL: s10107-012-0527-x
OpenAlex ID: W2038038281
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DOI: 10.1007/S10107-012-0527-X
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description: scientific article; zbMATH DE number 6160896