Iterative regularization methods for the multiple-sets split feasibility problem in Hilbert spaces. (English) Zbl 1513.47107
Summary: In this paper, we introduce iterative regularization methods for solving the multiple-sets split feasibility problem, that is to find a point closest to a family of closed convex subsets in one space such that its image under a bounded linear mapping will be closest to another family of closed convex subsets in the image space. We consider the cases, when the families are either finite or infinite. We also give two numerical examples for illustrating our main method.
MSC:
| 47J06 | Nonlinear ill-posed problems |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 49J30 | Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
Keywords:
nonexpansive mapping; fixed point; variational inequality; iterative regularisation; multiple-sets split feasibility problemReferences:
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