Smooth monotone stochastic variational inequalities and saddle point problems: A survey

Aleksandr Beznosikov; Boris Polyak; Eduard Gorbunov; Dmitry Kovalev; Alexander Gasnikov

doi:10.4171/mag/112

Smooth monotone stochastic variational inequalities and saddle point problems: A survey

Aleksandr Beznosikov, Boris Polyak, Eduard Gorbunov, Dmitry Kovalev, Alexander Gasnikov

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Abstract

This paper is a survey of methods for solving smooth, (strongly) monotone stochastic variational inequalities. To begin with, we present the deterministic foundation from which the stochastic methods eventually evolved. Then we review methods for the general stochastic formulation, and look at the finite-sum setup. The last parts of the paper are devoted to various recent (not necessarily stochastic) advances in algorithms for variational inequalities.

Original language	English (US)
Pages (from-to)	15-28
Number of pages	14
Journal	European Mathematical Society Magazine
Issue number	127
DOIs	https://doi.org/10.4171/mag/112
State	Published - Mar 22 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-03-28
Acknowledgements: The work was supported by Russian Science Foundation (project No. 21-71-30005).

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10.4171/mag/112

https://repository.kaust.edu.sa/bitstream/10754/680934/5/10.4171-mag-112.pdf

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author = "Aleksandr Beznosikov and Boris Polyak and Eduard Gorbunov and Dmitry Kovalev and Alexander Gasnikov",

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AU - Gasnikov, Alexander

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AB - This paper is a survey of methods for solving smooth, (strongly) monotone stochastic variational inequalities. To begin with, we present the deterministic foundation from which the stochastic methods eventually evolved. Then we review methods for the general stochastic formulation, and look at the finite-sum setup. The last parts of the paper are devoted to various recent (not necessarily stochastic) advances in algorithms for variational inequalities.

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Smooth monotone stochastic variational inequalities and saddle point problems: A survey

Abstract

Bibliographical note

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