A Randomized Algorithm for Generalized Accelerated Projection Method

We consider the convex feasibility problem, which is to determine a point in the intersection of a finite number of closed convex sets. It was shown in the past literature a so-called generalized acceleration method converges to a feasible point in the intersection of all the sets, assuming the intersection set has a nonempty interior. In this letter, we establish the same convergence result without any assumption on the interior of the feasible set. In particular, we devise a randomized accelerated projection algorithm and prove its linear convergence rate when all the convex sets are half-spaces in a finite-dimensional Euclidean space. Numerical experiments comparing the generalized acceleration method with the classic cyclic projection methods are presented, which justify the fast convergence rate and the out-performance of the proposed algorithm.