Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/7013
Title: Convergence of regularized time-stepping methods for differential variational inequalities
Authors: Chen, X 
Wang, Z
Keywords: Differential variational inequalities
P₀-function
Tikhonov regularization
Epi-convergence
Issue Date: 2013
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on optimization, 2013, v. 23, no. 3, p. 1647–1671 How to cite?
Journal: SIAM journal on optimization 
Abstract: This paper provides convergence analysis of regularized time-stepping methods for the differential variational inequality (DVI), which consists of a system of ordinary differential equations and a parametric variational inequality (PVI) as the constraint. The PVI often has multiple solutions at each step of a time-stepping method, and it is hard to choose an appropriate solution for guaranteeing the convergence. In [L. Han, A. Tiwari, M. K. Camlibel and J.-S. Pang, SIAM J. Numer. Anal., 47 (2009) pp. 3768--3796], the authors proposed to use “least-norm solutions” of parametric linear complementarity problems at each step of the time-stepping method for the monotone linear complementarity system and showed the novelty and advantages of the use of the least-norm solutions. However, in numerical implementation, when the PVI is not monotone and its solution set is not convex, finding a least-norm solution is difficult. This paper extends the Tikhonov regularization approximation to the P$_0$-function DVI, which ensures that the PVI has a unique solution at each step of the regularized time-stepping method. We show the convergence of the regularized time-stepping method to a weak solution of the DVI and present numerical examples to illustrate the convergence theorems.
URI: http://hdl.handle.net/10397/7013
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/120875223
Rights: © 2013 Society for Industrial and Applied Mathematics
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