An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem

Abstract

The multiple-set split feasibility problem (MSSFP), as a generalization of the split feasibility problem, is to find a point in the intersectionof a family of closed convex sets in one space such that its imageunder a linear transformation will be in the intersection of anotherfamily of closed convex sets in the image space. Censor et al. (2005) proposed a method for solving the multiple-set split feasibility problem (MSSFP), whose efficiency depends heavily on the step size, a fixed constant related to the Lipschitz constant of $\nabla p\left(x\right)$ which may be slow. Inthis paper, we present an accelerated algorithm by introducing anextrapolated factor to solve the multiple-set split feasibilityproblem. The framework encompasses the algorithm presented by Censoret al. (2005). The convergence of the method is investigated, and numerical experiments are provided to illustrate the benefits of the extrapolation.