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 - 11:20Room: 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
- Analysis and engineering of optimization algorithms
- Large- and Huge-scale optimization
Status: accepted
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