Modified parallel projection methods for the multivalued lexicographic variational inequalities using proximal operator in Hilbert spaces
In this paper, building upon projection methods and parallel splitting‐up techniques with using proximal operators, we propose new algorithms for solving the multivalued lexicographic variational inequalities in a real Hilbert space. First, the strong convergence theorem is shown with Lipschitz cont...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2020-04, Vol.43 (6), p.3260-3279 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Ngoc Anh, Pham Thi Hoai An, Le |
| description | In this paper, building upon projection methods and parallel splitting‐up techniques with using proximal operators, we propose new algorithms for solving the multivalued lexicographic variational inequalities in a real Hilbert space. First, the strong convergence theorem is shown with Lipschitz continuity of the cost mapping, but it must satisfy a strongly monotone condition. Second, the convergent results are also established to the multivalued lexicographic variational inequalities involving a finite system of demicontractive mappings under mild assumptions imposed on parameters. Finally, some numerical examples are developed to illustrate the behavior of our algorithms with respect to existing algorithms. |
| doi_str_mv | 10.1002/mma.6118 |
| format | Article |
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| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Algorithms Computer Science Convergence demicontractive mappings Estimates Hilbert space Inequalities Lipschitz continuous Mapping monotone projection methods multivalued lexicographic variational inequalities proximal operator |
| title | Modified parallel projection methods for the multivalued lexicographic variational inequalities using proximal operator in Hilbert spaces |
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