Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/30107
Title: Newton iterations in implicit time-stepping scheme for differential linear complementarity systems
Authors: Chen, X 
Xiang, S
Keywords: Differential linear complementarity problem
Generalized Newton method
Least-element solution
Least-norm solution
Nondegenerate matrix
Z-matrix
Issue Date: 2013
Source: Mathematical programming, 2013, v. 138, no. 1-2, p. 579-606 How to cite?
Journal: Mathematical Programming 
Abstract: We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping scheme for differential linear complementarity systems (DLCS). We choose a specific solution from the solution set of the linear complementarity constraints to define a locally Lipschitz continuous right-hand-side function in the differential equation. Moreover, we present a simple formula to compute an element in the Clarke generalized Jacobian of the solution function. We show that the implicit or semi-implicit time-stepping scheme using the generalized Newton method can be applied to a class of DLCS including the nondegenerate matrix DLCS and hidden Z-matrix DLCS, and has a superlinear convergence rate. To illustrate our approach, we show that choosing the least-element solution from the solution set of the Z-matrix linear complementarity constraints can define a Lipschitz continuous right-hand-side function with a computable Lipschitz constant. The Lipschitz constant helps us to choose the step size of the time-stepping scheme and guarantee the convergence.
URI: http://hdl.handle.net/10397/30107
ISSN: 0025-5610
DOI: 10.1007/s10107-012-0527-x
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