Solving strongly convex-concave composite saddle point problems with a small dimension of one of the variables

Egor, Gladin,; Kuruzov, Ilya; Stonyakin, Fedor; Pasechnyuk, Dmitry; Alkousa, Mohammad; Gasnikov, Alexander

doi:10.48550/arxiv.2010.02280

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2023

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“…Further deterministic "cutting-plane" improvements are connected with the additional assumptions about small dimension of the involved vectors x or/and y (see [43,44,91]) or with different structural (e.g., SPP on balls in 1-or ∞-norms) and sparsity assumptions, see e.g., [21,111,112] and references therein. Here lower bounds are mostly unknown.…”

Section: Recent Advancesmentioning

confidence: 99%

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

Beznosikov

Polyak²,

Gorbunov

et al. 2023

Eur. Math. Soc. Mag.

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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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