A class of methods for projection on the intersection of several ellipsoids

The paper is concerned with the basic optimization problem of projecting a point onto the intersection of several ellipsoids. 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 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 and to be very reliable and efficient in our testing.