Abstract
Abstract The projection algorithms for solving the constrained multiple-sets split feasibility problem are presented. The strong convergence results of the algorithms are given under some mild conditions. Especially, the minimum norm solution of the constrained multiple-sets split feasibility problem can be found.
Highlights
Let H and H be two real Hilbert spaces
A special case If N = M =, the multiple-sets split feasibility problem is reduced to the split feasibility problem which is formulated as finding a point x with the property x ∈ C and Ax ∈ Q
The split feasibility problem in finite-dimensional Hilbert spaces was first introduced by Censor and Elfving [ ] for modeling inverse problems which arise from phase retrievals and in medical image reconstruction [ ]
Summary
Let H and H be two real Hilbert spaces. Let C , C , . . . , CN be N nonempty closed convex subsets of H and let Q , Q , . . . , QM be M nonempty closed convex subsets of H. The multiple-sets split feasibility problem is formulated as follows: N The popular algorithm that solves the multiple-sets split feasibility problem and the split feasibility problem is Byrne’s CQ algorithm [ ] which is found to be a gradient-projection method in convex minimization. In this paper, we present the composite projection algorithms for solving the constrained multiple-sets split feasibility problem.
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