A new dynamical system with self-adaptive dynamical stepsize for pseudomonotone mixed variational inequalities
Xingxing Ju, Chuandong Li, Yu-Hong Dai, Jiawei Chen · Optimization · 2022
A new dynamical system with self-adaptive dynamical stepsize is introduced for solving pseudomonotone mixed variational inequalities (MVIs). The globally stable convergence results of the proximal dynamical systems for solving pseudomonotone MVIs are established under some mild conditions. The upper bound formula of the convergence time of the proposed proximal dynamical systems is independent of the initial conditions. The proposed proximal dynamical system is also applied to solve composite optimization problems and minimax optimization problems. Finally, numerical examples are presented to validate the effectiveness of the proposed methods.