Magyar tudományos akadémia

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Prof. Dr. Yurii Nesterov: High-Order Reduced -Gradient methods for Composite Variational Inequalities

Helyszín: DAB Székház

Prof. Dr. Yurii Nesterov
(CORE/INMA, Catholic University of Louvain (Belgium)
és CCOR, Corvinus Egyetem, (Budapest)

High-Order Reduced -Gradient methods for Composite Variational Inequalities

2024. február 14. (szerda) 16:00

MTA DAB Székház, Bognár Rezső Terem
4032 Debrecen, Thomas Mann u. 49.

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. Moreover, contrary to existing recipes, 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.