Decomposition dynamical systems for solving variational inequalities. (4th March 2023)

• Record Type: Journal Article
• Authors: Hai, Trinh Ngoc
• Is Part Of: Optimization. Volume 72:Number 3(2023)
• Page Start: 883
• Page End: 903
• Publication Date: 2023-03-04
• Subjects: Variational inequality -- equilibrium problem -- dynamical system -- decomposition algorithm -- convergence rate; 47J20 -- 49J40 -- 49M30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1995732
• Languages: English
• ISSNs: 0233-1934

Abstract

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.