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arXiv · 2307.03596

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

Zengzhen Tan·Rong Hu·Yaping Fang
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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.

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Zengzhen Tan, Rong Hu, Yaping Fang. 2023-07-07. A second order dynamical system method for solving a maximal comonotone inclusion problem. https://arxiv.org/abs/2307.03596

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