  The article is devoted to the development of numerical methods for solving
saddle point problems and variational inequalities with simplified requirements
for the smoothness conditions of functionals. Recently there were proposed some
notable methods for optimization problems with strongly monotone operators. Our
focus here is on newly proposed techniques for solving strongly convex-concave
saddle point problems. One of the goals of the article is to improve the
obtained estimates of the complexity of introduced algorithms by using
accelerated methods for solving auxiliary problems. The second focus of the
article is introducing an analogue of the boundedness condition for the
operator in the case of arbitrary (not necessarily Euclidean) prox structure.
We propose an analogue of the mirror descent method for solving variational
inequalities with such operators, which is optimal in the considered class of
problems.
