A von Neumann Alternating Method for Finding Common Solutions to Variational Inequalities

TL;DR

This paper introduces a modified von Neumann alternating projections algorithm to efficiently find common solutions to two variational inequalities in Hilbert space, advancing methods for solving CSVIP problems.

Contribution

The paper proposes a novel alternating method based on von Neumann's approach specifically designed for the CSVIP, focusing on two-set problems in Hilbert spaces.

Findings

The method effectively finds common solutions to two variational inequalities.

The approach extends von Neumann's projections to the CSVIP context.

The algorithm demonstrates convergence properties for the two-set case.

Abstract

Modifying von Neumann's alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.