An adaptive proximal method for variational inequalities

A novel analog of Nemirovski's proximal mirror method with an adaptive choice of constants in the minimized prox-mappings at each iteration for variational inequalities with a Lipschitz continuous field is proposed. Estimates of the number of iterations needed to attain the desired quality of solution of the variational inequality are obtained. It is shown how the proposed approach can be extended for the case of Hölder continuous field. A modification of the proposed algorithm for the case of an inexact oracle for the field operator is also considered.