An operator splitting method for monotone variational inequalities with a new perturbation strategy

In variational inequalities arising from applications such as engineering, economics and transportation, partial mappings are usually unknown, e.g., the demand function in traffic assignment problem. As a consequence, classical methods can not deal with this class of problems. On the other hand, the recently developed methods require restrictive conditions such as strong monotonicity of some mappings, which excludes many interesting applications. In this paper, we propose an operator splitting method with a new perturbation strategy for solving variational inequality problems with partially unknown mappings. Under the mild condition that the underlying mapping is monotone, we prove the global convergence of the method. We also report some preliminary numerical results which show that the new algorithm is also interesting from the numerical point of view.