Analytic Center Cutting Plane Methods for Variational Inequalities over Convex Bodies

TL;DR

This paper introduces analytic center cutting plane methods tailored for solving quasimonotone or pseudomonotone variational inequalities within convex bodies, extending applicability to both bounded and unbounded domains.

Contribution

It proposes novel analytic center cutting plane algorithms specifically designed for quasimonotone and pseudomonotone variational inequalities over convex bodies.

Findings

Algorithms effectively solve variational inequalities in bounded convex domains.

Methods extend to unbounded convex domains.

Potential improvements in convergence speed and robustness.

Abstract

An analytic center cutting plane method is an iterative algorithm based on the computation of analytic centers. In this paper, we propose some analytic center cutting plane methods for solving quasimonotone or pseudomonotone variational inequalities whose domains are bounded or unbounded convex bodies.