A Projected Stochastic Gradient Method for Finite-Sum Problems with Linear Equality Constraints

A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic gradient and a possibly inexact projection map. Under standard assumptions in the field of stochastic gradient methods, we provide theoretical results in agreement with the theory for unconstrained problems. Numerical results are presented to show the practical behavior of the procedure.