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An extrapolated iterative algorithm for multiple-set split feasibility problem. (English) Zbl 1243.49040
Summary: The Multiple-Set Split Feasibility problem (MSSFP), as a generalization of the split feasibility problem, is to find a point in the intersection of a family of closed convex sets in one space such that its image under a linear transformation will be in the intersection of another family of closed convex sets in the image space. In Y. Censor et al ”The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Probl. 21, No. 6, 2071-2084 (2005; Zbl 1089.65046)] a method is proposed for solving the 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. In this paper, we present an accelerated algorithm by introducing an extrapolated factor to solve the multiple-set split feasibility problem. The framework encompasses the algorithm presented by Censor [loc. cit.]. The convergence of the method is investigated, and numerical experiments are provided to illustrate the benefits of the extrapolation.
MSC:
 49M30 Other numerical methods in calculus of variations 90C25 Convex programming