  Abstract. The Set Intersection Problem (SIP) is the problem of finding a
point in the intersection of convex sets. This problem is typically solved by
the method of alternating projections. To accelerate the convergence, the idea
of using Quadratic Programming (QP) to project a point onto the intersection of
halfspaces generated by the projection process was discussed in earlier papers.
This paper looks at how one can integrate projection algorithms together with
an active set QP algorithm. As a byproduct of our analysis, we show how to
accelerate an SIP algorithm involving box constraints, and how to extend a
version of the Algebraic Reconstruction Technique (ART) while preserving finite
convergence. Lastly, the warmstart property of active set QP algorithms is a
valuable property for the problem of projecting onto the intersection of convex
sets.
