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

作者：Bot Radu Ioan^*; Csetnek Ernoe Robert

来源：Journal of Mathematical Analysis and Applications, 2016, 435(2): 1688-1700.

DOI：10.1016/j.jmaa.2015.11.032

• Dynamical systems
• Lyapunov analysis
• Monotone inclusions
• Forward-backward algorithm
• Penalty schemes

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.

• 出版日期2016-3-15