A Dynamical System Associated with the Fixed Points Set of a Nonexpansive Operator

作者：Bot Radu Ioan^*; Csetnek Ernoe Robert

来源：Journal of Dynamics and Differential Equations, 2017, 29(1): 155-168.

DOI：10.1007/s10884-015-9438-x

• Dynamical systems
• Lyapunov analysis
• Krasnosel'skii-Mann algorithm
• Monotone inclusions
• Forward-backward algorithm

We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying on Lyapunov analysis. We show also an order of convergence of for the fixed point residual of the trajectory of the dynamical system. We apply the results to dynamical systems associated with the problem of finding the zeros of the sum of a maximally monotone operator and a cocoercive one. Several dynamical systems from the literature turn out to be particular instances of this general approach.

• 出版日期2017-3