Stochastic heavy ball method for constrained stochastic optimization problems

Abstract

In this paper, we consider a heavy-ball method for the constrained stochastic optimization problem by focusing to the situation that the constraint set is specified as the intersection of possibly finitely many constraint sets. A variant algorithm of the stochastic heavy ball method is proposed which will be incrementally processed by both the stochastic heavy ball method and random constraint projection simultaneously. They converge almost surely to a solution of the suggested method is exhibited. Finally, a numerical experiment is discussed.