Decomposition dynamical systems for solving variational inequalities

ABSTRACT

In this paper, we propose two decomposition dynamical systems for solving strongly pseudomonotone variational inequalities given by a sum of two mappings. We prove that trajectories of these dynamical systems converge to the unique solution of the variational inequality. Also, we extend these algorithms for equilibrium problems and study their convergence rate. This approach is novel and the new algorithms can be considered as continuous-time versions of existing decomposition algorithms for variational inequalities and equilibrium problems.

KEYWORDS:

• Variational inequality
• equilibrium problem
• dynamical system
• decomposition algorithm
• convergence rate

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47J20
• 49J40
• 49M30

Acknowledgments

The author thanks the reviewer and the editor for their constructive comments which helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Vietnam Ministry of Education and Training [grant number B2020-BKA-21-CTTH].