2025/10/04 by Reza Rahimi Baghbadorani, Peyman Mohajerin Esfahani, Baghbadorani, Reza Rahimi +3
Computer Science · Engineering · #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2510.03842
openalex publication_date 2025/10/04 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28
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.