2022/01/04 by Radu Ioan Boţ, Bot, Radu Ioan, David Alexander Hulett +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2201.01017
openalex publication_date 2022/01/04 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator A and a cocoercive operator B. We study the asymptotic behaviour of the trajectories generated by a second order equation with vanishing damping, attached to this problem, and governed by a time-dependent forward-backward-type operator. This is a splitting system, as it only requires forward evaluations of B and backward evaluations of A. A proper tuning of the system parameters ensures the weak convergence of the trajectories to the set of zeros of A + B, as well as fast convergence of the velocities towards zero. A particular case of our system allows to derive fast convergence rates for the problem of minimizing the sum of a proper, convex and lower semicontinuous function and a smooth and convex function with Lipschitz continuous gradient. We illustrate the theoretical outcomes by numerical experiments.