An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem
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 co...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/149508 |
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| _version_ | 1832559941755338752 |
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| author | Yazheng Dang Yan Gao |
| author_facet | Yazheng Dang Yan Gao |
| author_sort | Yazheng Dang |
| collection | DOAJ |
| description | 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. 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 ∇p(x) 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
et al. (2005). The convergence of the method is investigated, and numerical experiments are provided to illustrate the benefits of the extrapolation. |
| format | Article |
| id | doaj-art-f8277ae0aef84c3dad15b60c962182be |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f8277ae0aef84c3dad15b60c962182be2025-02-03T01:28:59ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/149508149508An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility ProblemYazheng Dang0Yan Gao1School of Management, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Management, University of Shanghai for Science and Technology, Shanghai 200093, ChinaThe 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. 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 ∇p(x) 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 et al. (2005). The convergence of the method is investigated, and numerical experiments are provided to illustrate the benefits of the extrapolation.http://dx.doi.org/10.1155/2012/149508 |
| spellingShingle | Yazheng Dang Yan Gao An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem Abstract and Applied Analysis |
| title | An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem |
| title_full | An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem |
| title_fullStr | An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem |
| title_full_unstemmed | An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem |
| title_short | An Extrapolated Iterative Algorithm for Multiple-Set Split Feasibility Problem |
| title_sort | extrapolated iterative algorithm for multiple set split feasibility problem |
| url | http://dx.doi.org/10.1155/2012/149508 |
| work_keys_str_mv | AT yazhengdang anextrapolatediterativealgorithmformultiplesetsplitfeasibilityproblem AT yangao anextrapolatediterativealgorithmformultiplesetsplitfeasibilityproblem AT yazhengdang extrapolatediterativealgorithmformultiplesetsplitfeasibilityproblem AT yangao extrapolatediterativealgorithmformultiplesetsplitfeasibilityproblem |