On the Convergence of Classical Variational Inequality Algorithms
Author(s)Magnanti, Thomas L.; Perakis, Georgia
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.
Massachusetts Institute of Technology, Operations Research Center
Operations Research Center Working Paper;OR 280-93