An extra gradient Anderson-accelerated algorithm for pseudomonotone variational inequalities

TL;DR

This paper introduces an enhanced algorithm combining extra gradient, line search, and Anderson acceleration to efficiently solve pseudomonotone variational inequalities, demonstrating strong convergence and superior performance in various complex problems.

Contribution

It presents a novel algorithm that guarantees global convergence without requiring Lipschitz continuity or contractive conditions, improving upon existing methods.

Findings

Proves convergence of the proposed algorithm from any initial point.

Shows the algorithm outperforms traditional methods in numerical experiments.

Validates effectiveness across diverse problem types including PDEs and nonlinear complementarity.

Abstract

This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to have fast convergent rate. We prove that the sequence generated by the proposed algorithm from any initial point converges to a solution of the pseudomonotone variational inequality problem without assuming the Lipschitz continuity and contractive condition, which are used for convergence analysis of the extra gradient method and Anderson-accelerated method, respectively in existing literatures. Numerical experiments, particular emphasis on Harker-Pang problem, fractional programming, nonlinear complementarity problem and PDE problem with free boundary, are conducted to validate the effectiveness and good performance of the proposed algorithm comparing with the extra gradient method and Anderson-accelerated method.