A second order dynamical system method for solving a maximal comonotone inclusion problem

TL;DR

This paper introduces a second order dynamical system approach for efficiently finding zeros of maximal comonotone operators in Hilbert spaces, with proven convergence and practical numerical demonstrations.

Contribution

It proposes a novel second order dynamical system model for maximal comonotone inclusion problems, including convergence analysis and a discrete algorithm variant.

Findings

Proven existence and uniqueness of solutions

Fast convergence with proper parameter tuning

Numerical examples validate the approach

Abstract

In this paper a second order dynamical system model is proposed for computing a zero of a maximal comonotone operator in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of a strong global solution of the proposed dynamical system. A proper tuning of the parameters can allow us to establish fast convergence properties of the trajectories generated by the dynamical system. The weak convergence of the trajectory to a zero of the maximal comonotone operator is also proved. Furthermore, a discrete version of the dynamical system is considered and convergence properties matching to that of the dynamical system are established under a same framework. Finally, the validity of the proposed dynamical system and its discrete version is demonstrated by two numerical examples.