Approaching the solving of constrained variational inequalities via penalty term-based dynamical systems

We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on Lyapunov analysis and on the ergodic continuous version of the...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 435; no. 2; pp. 1688 - 1700
Main Authors: Boţ, Radu Ioan, Csetnek, Ernö Robert
Format: Journal Article
Language:English
Published: Elsevier Inc 15.03.2016
Subjects:
Dynamical systems
Forward–backward algorithm
Lyapunov analysis
Monotone inclusions
Penalty schemes
Lyapunov analysis
Penalty schemes
Monotone inclusions
Dynamical systems
Forward–backward algorithm
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on Lyapunov analysis and on the ergodic continuous version of the celebrated Opial Lemma we prove weak ergodic convergence of the orbits to a solution of the constrained variational inequality under investigation. If one of the operators involved satisfies stronger monotonicity properties, then strong convergence of the trajectories can be shown.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2015.11.032