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

2015/03/06 by Radu Ioan Boţ, Bot, Radu Ioan, Ernö Robert Csetnek +1 · 1 citation
Computer Science · Mathematics · #34G25 #47H05 #47J25 #90C25 #Contact Mechanics and Variational Inequalities #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1503.01871

openalex publication_date 2015/03/06 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We investigate the existence and uniqueness of (locally) absolutely\ncontinuous trajectories of a penalty term-based dynamical system associated to\na constrained variational inequality expressed as a monotone inclusion problem.\nRelying on Lyapunov analysis and on the ergodic continuous version of the\ncelebrated Opial Lemma we prove weak ergodic convergence of the orbits to a\nsolution of the constrained variational inequality under investigation. If one\nof the operators involved satisfies stronger monotonicity properties, then\nstrong convergence of the trajectories can be shown.\n

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