On systems of extended primal–dual variational inequalities

Abstract

We consider a system of variational inequalities, which can be regarded as an extension of a primal-dual variational inequality system and involves multi-valued mappings. This problem has a great number of applications in Economics, Operations Research, Mathematical Physics and other fields. We suggest this problem to be converted into a single variational inequality with constraints. The latter problem is proposed to be solved by splitting-type methods, whose convergence is proved under monotonicity assumptions.