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2504. High-Order Reduced-Gradient Methods for Composite Variational Inequalities
Invited abstract in session MC-32: Advances in Complexity of Convex and Nonconvex Problems, stream Advances in large scale nonlinear optimization.
Monday, 12:30-14:00Room: 41 (building: 303A)
Authors (first author is the speaker)
| 1. | Yurii Nesterov
|
| CORE, Université catholique de Louvain (UCL) |
Abstract
In this talk, we present a unified approach for constructing efficient methods for solving Variational Inequalities, presented in a composite form (CVI). This class of problems is close to the maximal one, which can be efficiently treated by numerical methods. At the same time, it is more difficult than the class of Convex Optimization Problems. All efficient methods for VI use an additional “extra-gradient” step. We propose a new interpretation of this step as a cutting plane for the optimal solution, reflecting the interaction of the monotone operator with the boundary of the feasible set. Contrary to the existing approaches, we introduce a universal extragradient step, which does not depend on the particular class of CVI. Consequently, our framework can be used for developing optimal methods for CVI, which are based on high-order oracles.
Keywords
- Continuous Optimization
- Convex Optimization
Status: accepted
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