On the Convergence of Classical Variational Inequality Algorithms

Abstract

In this paper, we establish global convergence results for projection and relaxation algorithms for solving variational inequality problems, and for the Frank-Wolfe algorithm for solving convex optimization problems defined over general convex sets. The analysis rests upon the condition of f-monotonicity,which we introduced in a previous paper, and which is weaker than the traditional strong monotonicity condition. As part of our development, we provide a new interpretation of a norm condition typically used for establishing convergence of linearization schemes. Applications of our results arize in uncongested as well as congested transportation networks.