Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Professor Yurii Nesterov,University of Louvain, Belgium
Inviter:	Professor Xin Liu
Title:	Modern methods for Variational Inequalities and Equilibrium Problems
Language:	Chinese
Time & Venue:	2023.08.03 16:30-17:30 Tencent Meeting: 373-3811-9197
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. 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.