The modified proximal point algorithm in Hadamard spaces
Abstract The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results e...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-05-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1713-z |
| _version_ | 1818324809023488000 |
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| author | Shih-sen Chang Lin Wang Ching-Feng Wen Jian Qiang Zhang |
| author_facet | Shih-sen Chang Lin Wang Ching-Feng Wen Jian Qiang Zhang |
| author_sort | Shih-sen Chang |
| collection | DOAJ |
| description | Abstract The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces. |
| first_indexed | 2024-12-13T11:34:29Z |
| format | Article |
| id | doaj.art-557271b783444364a5226ac9d5ae0b90 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-13T11:34:29Z |
| publishDate | 2018-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-557271b783444364a5226ac9d5ae0b902022-12-21T23:47:50ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-05-012018111010.1186/s13660-018-1713-zThe modified proximal point algorithm in Hadamard spacesShih-sen Chang0Lin Wang1Ching-Feng Wen2Jian Qiang Zhang3Center for General Education, China Medical UniversityCollege of Statistics and Mathematics, Yunnan University of Finance and EconomicsCenter for Fundamental Science, Kaohsiung Medical UniversityCollege of Statistics and Mathematics, Yunnan University of Finance and EconomicsAbstract The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.http://link.springer.com/article/10.1186/s13660-018-1713-zHadamard spaceCAT ( 0 ) $\operatorname{CAT}(0)$ spaceMoreau–Yosida resolventImplicit iterative ruleProximal point algorithmVariational inequality |
| spellingShingle | Shih-sen Chang Lin Wang Ching-Feng Wen Jian Qiang Zhang The modified proximal point algorithm in Hadamard spaces Journal of Inequalities and Applications Hadamard space CAT ( 0 ) $\operatorname{CAT}(0)$ space Moreau–Yosida resolvent Implicit iterative rule Proximal point algorithm Variational inequality |
| title | The modified proximal point algorithm in Hadamard spaces |
| title_full | The modified proximal point algorithm in Hadamard spaces |
| title_fullStr | The modified proximal point algorithm in Hadamard spaces |
| title_full_unstemmed | The modified proximal point algorithm in Hadamard spaces |
| title_short | The modified proximal point algorithm in Hadamard spaces |
| title_sort | modified proximal point algorithm in hadamard spaces |
| topic | Hadamard space CAT ( 0 ) $\operatorname{CAT}(0)$ space Moreau–Yosida resolvent Implicit iterative rule Proximal point algorithm Variational inequality |
| url | http://link.springer.com/article/10.1186/s13660-018-1713-z |
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