A second order dynamical system method for solving a maximal comonotone inclusion problem
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.
Cite
@article{arxiv.2307.03596,
title = {A second order dynamical system method for solving a maximal comonotone inclusion problem},
author = {Zengzhen Tan and Rong Hu and Yaping Fang},
journal= {arXiv preprint arXiv:2307.03596},
year = {2023}
}