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.

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.