EUROPT 2024
Abstract Submission

226. A Fast Optimistic Method for Monotone Variational Inequalities

Invited abstract in session FB-4: Large-scale optimization II, stream Large-scale optimization.

Friday, 10:05 - 11:20
Room: M:M

Authors (first author is the speaker)

1. Michael Sedlmayer
Faculty of Mathematics, University of Vienna
2. Dang-Khoa Nguyen
Ho Chi Minh City University of Science
3. Radu Ioan Bot
Faculty of Mathematics, University of Vienna

Abstract

We study monotone variational inequalities that can arise as optimality conditions for constrained convex optimization or convex-concave minimax problems and propose a novel algorithm that uses only one gradient/operator evaluation and one projection onto the constraint set per iteration. The algorithm, which we call fOGDA-VI, achieves a o(1/k) rate of convergence in terms of the restricted gap function as well as the natural residual for the last iterate. Moreover, we provide a convergence guarantee for the sequence of iterates to a solution of the variational inequality. These are the best theoretical convergence results for numerical methods for (only) monotone variational inequalities reported in the literature.

Keywords

Status: accepted


Back to the list of papers