A Sequential Constraint Method for Solving Variational Inequality over the Intersection of Fixed Point Sets

TL;DR

This paper introduces a sequential constraint algorithm to solve variational inequalities over intersections of fixed point sets, proving strong convergence of the solution sequence.

Contribution

The paper proposes a novel sequential constraint method with proven strong convergence for variational inequalities over fixed point set intersections.

Findings

Algorithm guarantees strong convergence to the solution.

Applicable to variational inequalities involving firmly nonexpansive operators.

Provides theoretical foundation for solving complex fixed point intersection problems.

Abstract

We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated sequence to the solution of the considered problem.