# Some adaptive analog of Yu. E. Nesterov's method for variational inequalities with a strongly monotone operator

## TL;DR

This paper introduces an adaptive version of Nesterov's method tailored for variational inequalities with strongly monotone operators, providing parameter estimates that improve solution quality over iterations.

## Contribution

It presents a novel adaptive algorithm for variational inequalities with strong monotonicity, extending Nesterov's method with new parameter estimation techniques.

## Key findings

- Derived estimates for solution quality based on iteration count
- Demonstrated effectiveness of the adaptive method for strongly monotone operators
- Extended Nesterov's method to adaptive settings

## Abstract

An adaptive analogue of the Yu. E. Nesterov method for variational inequalities with a strongly monotone operator is proposed. Some estimates are obtained for the parameters determining the quality of the solution of the variational inequality depending on the number of iterations.