A Class of Methods for Projection on a Convex Set

The paper is concerning about the basic optimization problem of projecting a point onto a convex set. We present a class of methods where the problem is reduced to a sequence of projections onto the intersection of several balls. The subproblems are much simpler and more tractable, but the main advantage is that, in so doing, we can avoid solving linear systems completely and thus the methods are very suitable for large scale problems. The methods have been shown to have nice convergence properties under Slater’s constraint qualification.