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On the Convergence of Classical Variational Inequality Algorithms

Author(s)
Magnanti, Thomas L.; Perakis, Georgia
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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.
Date issued
1993-05
URI
http://hdl.handle.net/1721.1/5201
Publisher
Massachusetts Institute of Technology, Operations Research Center
Series/Report no.
Operations Research Center Working Paper;OR 280-93

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