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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Bot, Radu Ioan¹  Csetnek, Ernoe Robert¹ 

[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria

关键词: Dynamical systems;    Lyapunov analysis;    Monotone inclusions;    Forward-backward algorithm;    Penalty schemes;   

DOI  :  10.1016/j.jmaa.2015.11.032

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free