On Dykstra's Iterative Fitting Procedure

Abstract

This paper shows that Dykstra's procedure for finding the $I$-projection onto the intersection of closed convex sets holds in general. It does this by first showing that each of the $I$-projections onto individual convex sets defined in Dykstra's iterative procedure exists and that no condition such as imposed by Dykstra is required to prove the convergence of the iterative procedure to a unique $I$-projection.