Non-Convex Split Feasibility Problems: Models, Algorithms and Theory
In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantages in different settings of the problem. For each model, we study relevant iter...
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| Format: | Article |
| Language: | English |
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Université de Montpellier
2020-10-01
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| Series: | Open Journal of Mathematical Optimization |
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| Online Access: | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.1/ |
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| author | Gibali, Aviv Sabach, Shoham Voldman, Sergey |
| author_facet | Gibali, Aviv Sabach, Shoham Voldman, Sergey |
| author_sort | Gibali, Aviv |
| collection | DOAJ |
| description | In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantages in different settings of the problem. For each model, we study relevant iterative algorithms, some of which are well-known in this area and some are new. All the studied methods, including the well-known CQ Algorithm, are proven to have global convergence guarantees in the non-convex setting under mild conditions on the problem’s data. |
| format | Article |
| id | doaj-art-b1b1fdde862241498a917bc66ed647f1 |
| institution | Kabale University |
| issn | 2777-5860 |
| language | English |
| publishDate | 2020-10-01 |
| publisher | Université de Montpellier |
| record_format | Article |
| series | Open Journal of Mathematical Optimization |
| spelling | doaj-art-b1b1fdde862241498a917bc66ed647f12025-02-07T14:02:13ZengUniversité de MontpellierOpen Journal of Mathematical Optimization2777-58602020-10-01111510.5802/ojmo.110.5802/ojmo.1Non-Convex Split Feasibility Problems: Models, Algorithms and TheoryGibali, Aviv0Sabach, Shoham1Voldman, Sergey2Department of Mathematics, ORT Braude College, Karmiel 2161002, Israel; The Center for Mathematics and Scientific Computation, University of Haifa, Mt. Carmel, Haifa 3498838, IsraelFaculty of Industrial Engineering and Management, The Technion, Haifa, 3200003, IsraelFaculty of Industrial Engineering and Management, The Technion, Haifa, 3200003, IsraelIn this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantages in different settings of the problem. For each model, we study relevant iterative algorithms, some of which are well-known in this area and some are new. All the studied methods, including the well-known CQ Algorithm, are proven to have global convergence guarantees in the non-convex setting under mild conditions on the problem’s data.https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.1/Split feasibility problemsnon-convex minimizationconvergence analysisconstrained minimizationCQ algorithm |
| spellingShingle | Gibali, Aviv Sabach, Shoham Voldman, Sergey Non-Convex Split Feasibility Problems: Models, Algorithms and Theory Open Journal of Mathematical Optimization Split feasibility problems non-convex minimization convergence analysis constrained minimization CQ algorithm |
| title | Non-Convex Split Feasibility Problems: Models, Algorithms and Theory |
| title_full | Non-Convex Split Feasibility Problems: Models, Algorithms and Theory |
| title_fullStr | Non-Convex Split Feasibility Problems: Models, Algorithms and Theory |
| title_full_unstemmed | Non-Convex Split Feasibility Problems: Models, Algorithms and Theory |
| title_short | Non-Convex Split Feasibility Problems: Models, Algorithms and Theory |
| title_sort | non convex split feasibility problems models algorithms and theory |
| topic | Split feasibility problems non-convex minimization convergence analysis constrained minimization CQ algorithm |
| url | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.1/ |
| work_keys_str_mv | AT gibaliaviv nonconvexsplitfeasibilityproblemsmodelsalgorithmsandtheory AT sabachshoham nonconvexsplitfeasibilityproblemsmodelsalgorithmsandtheory AT voldmansergey nonconvexsplitfeasibilityproblemsmodelsalgorithmsandtheory |