On the Convergence of Projection Methods: Application to the Decomposition of Affine Variational Inequalities

摘要

In this paper, we, first discuss the global convergence of symmetric projection methods for solving nonlinear monotone vadational inequalities under a cocoercivity assumption. A similar analysis is applied to asymmetric projection methods, when the mapping is affine and monotone. Under a suitable choice orthe projection matrix, decomposition can be achieved. It is proved that this scheme achieves a linear convergence rate, thus enhancing results previously obtained by Tseng (Ref.1) and by Iuo and Tseng (ReT. 2).