On the Convergence of Classical Variational Inequality Algorithms
Name
OR-280-93.pdf
Size
1.95 MB
Format
Adobe PDF
Checksum (MD5)
1be2ed207b971d6fe641b18803b72422
Author(s)
Magnanti, Thomas L.
Perakis, Georgia
Date Issued
May 1993
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 280-93
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.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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