Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem
The multiple-set split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where c...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/927530 |
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| _version_ | 1841524859673247744 |
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| author | Yonghong Yao Rudong Chen Giuseppe Marino Yeong Cheng Liou |
| author_facet | Yonghong Yao Rudong Chen Giuseppe Marino Yeong Cheng Liou |
| author_sort | Yonghong Yao |
| collection | DOAJ |
| description | The multiple-set split feasibility problem requires finding a point closest to a
family of closed convex sets in one space such that its image under a linear transformation
will be closest to another family of closed convex sets in the image space.
It can be a model for many inverse problems where constraints are imposed on the
solutions in the domain of a linear operator as well as in the operator’s range. It
generalizes the convex feasibility problem as well as the two-set split feasibility
problem. In this paper, we will review and report some recent results on iterative approaches
to the multiple-set split feasibility problem. |
| format | Article |
| id | doaj-art-56c7ef7296b0492c8f606ef9ef5c1a00 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-56c7ef7296b0492c8f606ef9ef5c1a002025-02-03T05:47:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/927530927530Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility ProblemYonghong Yao0Rudong Chen1Giuseppe Marino2Yeong Cheng Liou3Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaDipartimento di Matematica, Università della Calabria, 87036 Arcavacata di Rende, ItalyDepartment of Information Management, Cheng Shiu University, Kaohsiung 833, TaiwanThe multiple-set split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator’s range. It generalizes the convex feasibility problem as well as the two-set split feasibility problem. In this paper, we will review and report some recent results on iterative approaches to the multiple-set split feasibility problem.http://dx.doi.org/10.1155/2012/927530 |
| spellingShingle | Yonghong Yao Rudong Chen Giuseppe Marino Yeong Cheng Liou Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem Journal of Applied Mathematics |
| title | Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem |
| title_full | Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem |
| title_fullStr | Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem |
| title_full_unstemmed | Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem |
| title_short | Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem |
| title_sort | applications of fixed point and optimization methods to the multiple set split feasibility problem |
| url | http://dx.doi.org/10.1155/2012/927530 |
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