Extrapolated Sequential Constraint Method for Variational Inequality over the Intersection of Fixed-Point Sets

TL;DR

This paper introduces an accelerated extrapolated sequential constraint method for solving variational inequalities over intersections of fixed-point sets, demonstrating strong convergence and improved numerical performance.

Contribution

It proposes a novel extrapolated sequential constraint method combining conjugate gradient and cyclic cutter ideas, with proven convergence and superior efficiency.

Findings

Method converges strongly under suitable step-size conditions.

Numerical experiments show improved efficiency over existing methods.

Applicable to variational inequalities with complex constraint intersections.

Abstract

This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each iteration, the proposed method is updated based on the ideas of a hybrid conjugate gradient method used to accelerate the well-known hybrid steepest descent method, and an extrapolated cyclic cutter method for solving a common fixed point problem. We prove strong convergence of the method under some suitable assumptions of step-size sequences. We finally show the numerical efficiency of the proposed method compared to some existing methods.