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This paper deals with the convex feasibility problem, where the feasible setis given as the intersection of a (possibly infinite) number of closed convexsets. We assume that each set is specified algebraically as a convexinequality, where the associated convex function is general (possiblynon-differentiable). For finding a point satisfying all the convex inequalitieswe design and analyze random projection algorithms using special subgradientiterations and extrapolated stepsizes. Moreover, the iterate updates areperformed based on parallel random observations of several constraintcomponents. For these minibatch stochastic subgradient-based projection methodswe prove sublinear convergence results and, under some linear regularitycondition for the functional constraints, we prove linear convergence rates. Wealso derive conditions under which these rates depend explicitly on theminibatch size. To the best of our knowledge, this work is the first derivingconditions that show when minibatch stochastic subgradient-based projectionupdates have a better complexity than their single-sample variants.

Minibatch stochastic subgradient-based projection algorithms for solving convex inequalities