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

作     者：Bot, Radu Ioan Csetnek, Ernoe Robert 

作者机构：Univ Vienna Fac Math A-1090 Vienna Austria 

出 版 物：《JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS》 (数学分析与应用杂志)

年 卷 期：2016年第435卷第2期

页      面：1688-1700页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：DFG (German Research Foundation) [BO 2516/4-1] FWF (Austrian Science Fund), Lise Meitner Programme [M 1682-N25] Austrian Science Fund (FWF) [M1682] Funding Source: Austrian Science Fund (FWF) 

主　　题：Dynamical systems Lyapunov analysis Monotone inclusions Forward-backward algorithm Penalty schemes 

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.