A successive projection method

It is of both theoretical and practical interest to find the projection of a point to the intersection of a finite number of closed convex sets by a sequence of projections to the individual sets successively. In this paper we study such a method and analyze its convergence properties. A main feature of the method is its capability to decompose the projection problem into several small ones. For some structured sparse problems these small subproblems can be solved independently and the presented method has a potential use in parallel computation.This material is based on work supported in part by the National Science Foundation under Grant DMS-8602419 and by the Center for Supercomputing Research and Development, University of Illinois.