Web: http://arxiv.org/abs/2204.09228

May 11, 2022, 1:12 a.m. | Yang Cai, Argyris Oikonomou, Weiqiang Zheng

cs.LG updates on arXiv.org arxiv.org

The monotone variational inequality is a central problem in mathematical
programming that unifies and generalizes many important settings such as smooth
convex optimization, two-player zero-sum games, convex-concave saddle point
problems, etc. The extragradient algorithm by Korpelevich [1976] and the
optimistic gradient descent-ascent algorithm by Popov [1980] are arguably the
two most classical and popular methods for solving monotone variational
inequalities. Despite its long history, the following major problem remains
open. What is the last-iterate convergence rate of the extragradient algorithm …

algorithm arxiv convergence gradient math

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