Smooth monotone stochastic variational inequalities and saddle point problems: A survey
Aleksandr Beznosikov, B. T. Polyak, Eduard Gorbunov, Dmitry Kovalev, Alexander Gasnikov
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.
Topics & Concepts
Variational inequalityMonotone polygonSaddle pointMathematicsApplied mathematicsInequalityStochastic optimizationSaddleMathematical optimizationPoint (geometry)Mathematical economicsMathematical analysisGeometryOptimization and Variational AnalysisRisk and Portfolio OptimizationPoint processes and geometric inequalities