Two hybrid conjugate gradient based algorithms on Riemannian manifolds with adaptive restart strategy for nonconvex optimization problems
In this paper, we propose two hybrid conjugate gradient algorithms for solving nonconvex optimization problems on Riemannian manifolds. The conjugate parameter of the first method extends a hybrid formula [Comput. Oper. Res. 159 (2023) 106341] from Euclidean to Riemannian spaces. The conjugate param...
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| Vydáno v: | Journal of computational and applied mathematics Ročník 461; s. 116452 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.06.2025
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| ISSN: | 0377-0427 |
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| Abstract | In this paper, we propose two hybrid conjugate gradient algorithms for solving nonconvex optimization problems on Riemannian manifolds. The conjugate parameter of the first method extends a hybrid formula [Comput. Oper. Res. 159 (2023) 106341] from Euclidean to Riemannian spaces. The conjugate parameter of the second method integrates the Fletcher–Reeves conjugate parameter with another flexible conjugate parameter. An adaptive restart strategy is then incorporated into their respective search directions to enhance their theoretical properties and computational efficiency. As a result, both methods independently generate sufficient descent directions regardless of any stepsize strategy on Riemannian manifolds. Under typical assumptions and using the Riemannian weak Wolfe conditions to generate stepsize, the global convergence results of these two families are demonstrated. Numerical comparisons with existing methods using different Riemannian optimization scenarios verify the effectiveness of our proposed methods. |
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| AbstractList | In this paper, we propose two hybrid conjugate gradient algorithms for solving nonconvex optimization problems on Riemannian manifolds. The conjugate parameter of the first method extends a hybrid formula [Comput. Oper. Res. 159 (2023) 106341] from Euclidean to Riemannian spaces. The conjugate parameter of the second method integrates the Fletcher–Reeves conjugate parameter with another flexible conjugate parameter. An adaptive restart strategy is then incorporated into their respective search directions to enhance their theoretical properties and computational efficiency. As a result, both methods independently generate sufficient descent directions regardless of any stepsize strategy on Riemannian manifolds. Under typical assumptions and using the Riemannian weak Wolfe conditions to generate stepsize, the global convergence results of these two families are demonstrated. Numerical comparisons with existing methods using different Riemannian optimization scenarios verify the effectiveness of our proposed methods. |
| ArticleNumber | 116452 |
| Author | Jiang, Meixuan Wang, Yun Shao, Hu Wu, Ting Sun, Weiwei |
| Author_xml | – sequence: 1 givenname: Meixuan surname: Jiang fullname: Jiang, Meixuan organization: School of Mathematics, Jiangsu Center for Applied Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China – sequence: 2 givenname: Yun surname: Wang fullname: Wang, Yun organization: School of Mathematics, Jiangsu Center for Applied Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China – sequence: 3 givenname: Hu orcidid: 0000-0001-7816-0707 surname: Shao fullname: Shao, Hu email: shaohu@cumt.edu.cn organization: School of Mathematics, Jiangsu Center for Applied Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China – sequence: 4 givenname: Ting surname: Wu fullname: Wu, Ting email: tingwu@nju.edu.cn organization: School of Mathematics, Nanjing University, Nanjing 210093, Jiangsu, China – sequence: 5 givenname: Weiwei surname: Sun fullname: Sun, Weiwei organization: School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, Anhui, China |
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| Cites_doi | 10.1007/s11075-022-01448-y 10.1016/j.apm.2023.01.018 10.1007/s10589-020-00224-9 10.1016/j.apm.2014.08.008 10.1016/j.aml.2010.08.002 10.1137/110845768 10.1093/comjnl/7.2.149 10.1016/0041-5553(69)90035-4 10.1016/j.cam.2022.114879 10.1007/s11075-023-01527-8 10.1016/j.camwa.2018.10.002 10.1007/BF01580369 10.1080/10556780701223293 10.1007/s41980-021-00647-y 10.1137/11082885X 10.1109/ICASSP.2006.1661433 10.1016/j.cor.2023.106341 10.1093/imanum/drac018 10.1080/10556788.2023.2189718 10.1016/j.cam.2007.04.028 10.1007/s40305-020-00295-9 10.1023/B:NUMA.0000021761.10993.6e 10.1007/s12190-022-01772-5 10.1137/0802003 10.1007/BF00939455 10.1080/10556788.2024.2364203 10.1137/S1052623497318992 10.3390/math9121353 10.4153/CJM-1965-053-6 10.1007/s10915-019-00971-w 10.1007/s12190-022-01713-2 10.1007/s12190-021-01622-w 10.1147/rd.164.0431 10.1007/s101070100263 10.1007/BF00940464 10.1007/BF02871976 10.1080/02331934.2013.836650 10.6028/jres.049.044 10.1016/j.apnum.2024.06.020 10.1007/s10589-016-9883-4 10.1007/BF00939927 10.1007/s11075-022-01495-5 10.1007/s10957-021-01874-3 10.1023/A:1012930416777 10.1007/s40314-021-01557-9 |
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| Keywords | Global convergence Hybrid conjugate gradient method Riemannian optimization Adaptive restart strategy |
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| Title | Two hybrid conjugate gradient based algorithms on Riemannian manifolds with adaptive restart strategy for nonconvex optimization problems |
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