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. Convergence of the dis...

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Bibliographic Details
Published in:Set-valued and variational analysis 2019-06, Vol.27 (2), p.433-468
Main Authors: Hintermüller, M., Rautenberg, C. N., Strogies, N.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Computational geometry
Convexity
Discretization
Mathematical analysis
Mathematics
Mathematics and Statistics
Optimization
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Summary: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. 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.
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-018-0489-0