A first order dynamical system and its discretization for a class of variational inequalities

In this paper, we study the variational inequality problem over the set of common fixed points of a Lipschitz continuous pseudo-contraction and a finite family of strictly pseudo-contractive operators on a real Hilbert space. We introduce a first order dynamical system in accordance with the Lavrentiev regularization method. The existence and strong convergence with a discretized variant of the trajectory of the dynamical system are proved under some mild conditions. Applications to solving the convex constrained monotone equations and to the LASSO problem with numerical experiments are given for validating our results.