On the convergence of projection methods: Application to the decomposition of affine variational inequalities (Q1897456)

We first discuss the global convergence of symmetric projection methods for solving nonlinear monotone variational 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 of the projection matrix, decomposition can be achieved. It is proved that this scheme achieves a linear convergence rate, thus enhancing results previously obtained by \textit{P. Tseng} [SIAM J. Control Optimization 29, No. 1, 119-138 (1991; Zbl 0737.90048)] and \textit{Z.-Q. Luo} and \textit{P. Tseng} [SIAM J. Optim. 2, No. 1, 43-54 (1992; Zbl 0777.49010)].