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http://hdl.handle.net/10397/7013
Title: | Convergence of regularized time-stepping methods for differential variational inequalities | Authors: | Chen, X Wang, Z |
Issue Date: | 2013 | Source: | SIAM journal on optimization, 2013, v. 23, no. 3, p. 1647–1671 | 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. | Keywords: | Differential variational inequalities P₀-function Tikhonov regularization Epi-convergence |
Publisher: | Society for Industrial and Applied Mathematics | Journal: | SIAM journal on optimization | ISSN: | 1052-6234 | EISSN: | 1095-7189 | DOI: | 10.1137/120875223 | Rights: | © 2013 Society for Industrial and Applied Mathematics |
Appears in Collections: | Journal/Magazine Article |
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Chen_Convergence_Regularized_Time-stepping.pdf | 467.57 kB | Adobe PDF | View/Open |
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