A dynamic distributed conjugate gradient method for variational inequality problem over the common fixed-point constraints

In this paper, we propose a dynamic distributed conjugate gradient method for solving the strongly monotone variational inequality problem over the intersection of fixed-point sets of firmly nonexpansive operators. The proposed method allows the independent computation of a firmly nonexpansive operator along with the dynamic weight which is updated at each iteration. This strategy aims to speed up the convergence behavior of the algorithm by updating control factors to drive each iterative step. Under some suitable control conditions on corresponding parameters, we show a strong convergence of the iterate to the unique solution of the considered variational inequality problem. We consider the numerical experiments and discuss some observation points by applying the model to solve the image classification problem via the support vector machine learning.