Strong convergence of expected-projection methods in hilbert spaces

Abstract

Projection methods are iterative algorithms for computing common points of convex sets. They proceed via successive or simultaneous projections onto the given sets. Expected-projection methods, as defined in this work, generalize the simultaneous projection methods. We prove under quite mild conditions, that expected-projection methods in Hilbert spaces converge strongly to almost common points of infinite families of convex sets provided that such points exist. Relying on this result we show how expected-projection methods can be used to solve significant problems of applied mathematics.