  The article is devoted to the development of numerical methods for solving
variational inequalities with relatively strongly monotone operators. We
consider two classes of variational inequalities related to some analogs of the
Lipschitz condition of the operator that appeared several years ago. One of
these classes is associated with the relative boundedness of the operator, and
the other one with the analog of the Lipschitz condition (namely, relative
smoothness). For variational inequalities with relatively bounded and
relatively strongly monotone operators, we introduce a modification of the
Mirror Descent method, which optimizes the convergence rate. We also propose
the adaptive Proximal Pirror algorithm and its restarted version with a linear
convergence rate for problems with relatively smooth and relatively strongly
monotone operators.
