Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem
In this paper, we study an iterative method for solving the multiple-set split feasibility problem: find a point in the intersection of a finite family of closed convex sets in one space such that its image under a linear transformation belongs to the intersection of another finite family of closed...
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| Format: | Article |
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MDPI AG
2020-07-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/25/3/47 |
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| author | Guash Haile Taddele Poom Kumam Anteneh Getachew Gebrie Kanokwan Sitthithakerngkiet |
| author_facet | Guash Haile Taddele Poom Kumam Anteneh Getachew Gebrie Kanokwan Sitthithakerngkiet |
| author_sort | Guash Haile Taddele |
| collection | DOAJ |
| description | In this paper, we study an iterative method for solving the multiple-set split feasibility problem: find a point in the intersection of a finite family of closed convex sets in one space such that its image under a linear transformation belongs to the intersection of another finite family of closed convex sets in the image space. In our result, we obtain a strongly convergent algorithm by relaxing the closed convex sets to half-spaces, using the projection onto those half-spaces and by introducing the extended form of selecting step sizes used in a relaxed CQ algorithm for solving the split feasibility problem. We also give several numerical examples for illustrating the efficiency and implementation of our algorithm in comparison with existing algorithms in the literature. |
| first_indexed | 2024-03-10T18:13:44Z |
| format | Article |
| id | doaj.art-25d62dbd57b6473b8c785f322453d720 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T18:13:44Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-25d62dbd57b6473b8c785f322453d7202023-11-20T07:51:14ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472020-07-012534710.3390/mca25030047Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility ProblemGuash Haile Taddele0Poom Kumam1Anteneh Getachew Gebrie2Kanokwan Sitthithakerngkiet3Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, ThailandDepartment of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, ThailandDepartment of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan P.O. Box 445, EthiopiaIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, ThailandIn this paper, we study an iterative method for solving the multiple-set split feasibility problem: find a point in the intersection of a finite family of closed convex sets in one space such that its image under a linear transformation belongs to the intersection of another finite family of closed convex sets in the image space. In our result, we obtain a strongly convergent algorithm by relaxing the closed convex sets to half-spaces, using the projection onto those half-spaces and by introducing the extended form of selecting step sizes used in a relaxed CQ algorithm for solving the split feasibility problem. We also give several numerical examples for illustrating the efficiency and implementation of our algorithm in comparison with existing algorithms in the literature.https://www.mdpi.com/2297-8747/25/3/47multiple-set split feasibility problemrelaxed CQ algorithmsubdifferentialstrong convergenceHilbert space |
| spellingShingle | Guash Haile Taddele Poom Kumam Anteneh Getachew Gebrie Kanokwan Sitthithakerngkiet Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem Mathematical and Computational Applications multiple-set split feasibility problem relaxed CQ algorithm subdifferential strong convergence Hilbert space |
| title | Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem |
| title_full | Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem |
| title_fullStr | Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem |
| title_full_unstemmed | Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem |
| title_short | Half-Space Relaxation Projection Method for Solving Multiple-Set Split Feasibility Problem |
| title_sort | half space relaxation projection method for solving multiple set split feasibility problem |
| topic | multiple-set split feasibility problem relaxed CQ algorithm subdifferential strong convergence Hilbert space |
| url | https://www.mdpi.com/2297-8747/25/3/47 |
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