Several acceleration schemes for solving the multiple-sets split feasibility problem

In this paper we present several acceleration schemes for solving the multiple-sets split feasibility problem (MSFP), which is to find a point which belongs to the intersection of a family of closed convex sets in one space, such that its image under a linear transformation belongs to the intersection of another family of closed convex sets in the image space. We first modify the existing method and give a self-adaptive algorithm to solve the MSFP, which computes the step-size by Armijo-like searches and performs an additional projection step onto some simple closed convex set X⊆RN at each iteration; then we present a special case of this algorithm. Convergence results are analyzed, and further discussions on accelerating relaxed algorithms are lead. Preliminary numerical experiments shows that these accelerating schemes are practical and promising for solving the MSFPs.