Some Adaptive First-Order Methods for Variational Inequalities with Relatively Strongly Monotone Operators and Generalized Smoothness

In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, focus on the modification of recently proposed, in smooth case [18], numerical method generalized (with Hölder condition) saddle point problem, which has convergence rate estimates similar to accelerated methods. We provide motivation such an approach and obtain theoretical results proposed method. Our second is adaptation widespread The key idea our refusal well-known restart technique, cases causes difficulties implementing algorithms applied problems. Nevertheless, show a comparable respect based above-mentioned technique. Also, present experiments, demonstrate effectiveness