A Frank-Wolfe algorithm for strongly monotone variational inequalities
R. Rahimi Baghbadorani (TU Delft - Team Sergio Grammatico)
P. Mohajerin Esfahani (TU Delft - Team Peyman Mohajerin Esfahani, University of Toronto)
S. Grammatico (TU Delft - Team Sergio Grammatico)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
We propose an accelerated algorithm with a Frank-Wolfe method as an oracle for solving strongly monotone variational inequality problems. While standard solution approaches, such as projected gradient descent (aka value iteration), involve projecting onto the desired set at each iteration, a distinctive feature of our proposed method is the use of a linear minimization oracle in each iteration. This difference potentially reduces the projection cost, a factor that can become significant for certain sets or in high-dimensional problems. We validate the performance of the proposed algorithm on the traffic assignment problem, motivated by the fact that the projection complexity per iteration increases exponentially with respect to the number of links.
help_outline