Proximal projection methods for variational inequalities and Cesaro averaged approximations
In this paper, we prove convergence and stability of Cesaro averages generated by the proximal projection method applied to nonlinear equations and variational inequalities in uniformly convex and uniformly smooth Banach spaces. We first consider the stability of the approximations with respect to perturbations of the operator and constraint sets. Weak convergence of Cesaro averages is shown to hold with only a monotonicity condition for the operator involved. If in addition, proximal iterations are also satisfying some boundedness requirements, then we show that the weak convergence of Cesaro averages is stable. (C) 2002 Elsevier Science Ltd. All rights reserved.
variational inequality stability banach space monotone operators prox-projection method normalized duality mapping metric and generalized projection operators lyapunov functionals young-fenchel transformation cesaro averaged convergence