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The article is devoted to some adaptive methods for variational inequalitieswith relatively smooth and relatively strongly monotone operators. Startingfrom the recently proposed proximal variant of the extragradient method forthis class of problems, we investigate in detail the method with adaptivelyselected parameter values. An estimate of the convergence rate of this methodis proved. The result is generalized to a class of variational inequalitieswith relatively strongly monotone generalized smooth variational inequalityoperators. Numerical experiments have been performed for the problem of ridgeregression and variational inequality associated with box-simplex games.

Adaptive Methods or Variational Inequalities with Relatively Smooth and Reletively Strongly Monotone Operators