# The effective implementation of an accelerated method for solving variational inequalities

## Abstract

A nonlocally converging algorithm for solving variational inequalities with strongly monotone operator and convex constraints-inequalities has been constructed. The algorithm has a high rate of convergence. The method is based on a combination of the global first-order algorithm that uses an iterative sequence in the space of direct variables with Newton's method of solving the Kuhn-Tucker conditions of variational inequalities in the neighborhood of the solution. The effective implementation of the proposed algorithm has been performed. The computational aspects associated with the two time-consuming sub-tasks of a presented algorithm — the quadratic programming problem and solving a system of nonlinear equations have been considered. The implementation of the method has been tested by solving the variational inequalities with a nonpotential operator. A comparative analysis of the accelerated algorithm and the first order algorithm has been performed. The high convergence of the proposed algorithm has been confirmed by the results of computational experiments.

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