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Dissipative and Non-dissipative Evolutionary Quasi-variational Inequalities with Gradient Constraints

  • Evolutionary quasi-variational inequality (QVI) problems of dissipative and non-dissipative nature with pointwise constraints on the gradient are studied. A semi-discretization in time is employed for the study of the problems and the derivation of a numerical solution scheme, respectively. Convergence of the discretization procedure is proven and properties of the original infinite dimensional problem, such as existence, extra regularity and non-decrease in time, are derived. The proposed numerical solver reduces to a finite number of gradient-constrained convex optimization problems which can be solved rather efficiently. The paper ends with a report on numerical tests obtained by a variable splitting algorithm involving different nonlinearities and types of constraints.
Metadaten
Author:Michael Hintermüller, Carlos Rautenberg, Nikolai Strogies
Parent Title (German):Set-Valued and Variational Analysis
Document Type:Article
Language:English
Date of Publication (online):2017/10/31
Date of first Publication:2017/10/31
Release Date:2017/10/31
Volume:27
First Page:433
Last Page:468
Institutes:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B02