Combined partial regularization and descent method for a generalized primal-dual system

Abstract

A variational inequality system, which is a generalization of the saddle point problem, is considered. The system does not possess monotonicity properties and the feasible set is unbounded in general. To solve the problem we propose a completely implementable iterative scheme, whose convergence is proved under certain coercivity type conditions. © 2012 Springer-Verlag.