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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| Published in: | Journal of computational and applied mathematics Vol. 461; p. 116452 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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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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| References | Hu, Storey (b15) 1991; 71 Wang, Yuan, Pang (b11) 2022; 93 Hu, Liu, Wen, Yuan (b40) 2020; 8 Townsend, Koep, Weichwald (b50) 2016; 17 Jian, Han, Jiang (b16) 2015; 39 Shao, Guo, Wu, Liu (b20) 2023; 118 Motzkin, Straus (b54) 1965; 17 Dai, Yuan (b6) 1999; 10 Zhang, Zhou (b28) 2008; 216 Jian, Chen, Jiang, Liu (b14) 2022; 68 P.-A. Absil, K.A. Gallivan, Joint diagonalization on the oblique manifold for independent component analysis, in: 2006 IEEE International Conference on Acoustics, Speech and Signal Processing Proceedings, vol. 5, 2006, p. V. Crowder, Wolfe (b31) 1972; 16 Absil, Mahony, Sepulchre (b39) 2008 Zhang, Zhou, Li (b10) 2007; 22 Andrei (b35) 2011; 34 Zhu (b44) 2017; 67 Liu, Yuan, Zhuo, Shao (b17) 2024; 36 Dai, Yuan (b27) 2001; 103 Touati-Ahmed, Storey (b25) 1990; 64 Hestenes, Stiefel (b2) 1952; 49 Sakai, Iiduka (b29) 2020; 77 Liu, Shao, Yuan, Wu, Zheng (b12) 2023; 94 Gilbert, Nocedal (b26) 1992; 2 Dolan, Moré (b49) 2002; 91 Polyak (b3) 1969; 9 Tian, Wang, Pang, Zhang, Meng (b13) 2021; 9 Chen, Shao, Liu, Li, Rong (b18) 2024; 204 Jiang, Jian, Song, Liu (b7) 2021; 40 Zoutendijk (b48) 1970 Jian, Liu, Jiang, Zhang (b24) 2022; 68 Deng, Peng (b37) 2022; 43 Fletcher, Reeves (b1) 1964; 7 Wu, Shao, Liu, Zhang, Zhuo (b9) 2023; 422 Peng, Wu, Hu, Deng (b38) 2023; 88 Sato (b41) 2021 Sato, Iwai (b46) 2015; 64 Liu, Storey (b5) 1991; 69 Vandereycken (b51) 2013; 23 Fletcher (b4) 1987 Smith (b43) 1994; 3 Dai, Yuan (b33) 1998; 41 Jiang, Ye, Huang, Liu (b36) 2023; 159 Tang, Tan, Xing, Zheng (b42) 2023; 94 Yuan, Gu, Lai, Wen (b53) 2019; 2 Wan, Yang, Wang (b21) 2011; 24 Ring, Wirth (b47) 2012; 22 Dai, Liao, Li (b34) 2004; 35 Jian, Liu, Jiang, He (b8) 2022; 48 Powell (b32) 1976; 11 Shao, Guo, Wu, Liu (b23) 2023; 118 Liu, Feng, Zou (b22) 2019; 77 Tang, Rong, Jian, Xing (b45) 2023; 69 Sakai, Iiduka (b30) 2021; 190 Jiang, Yang, Jian, Wu (b19) 2023; 38 Jiang (10.1016/j.cam.2024.116452_b36) 2023; 159 Peng (10.1016/j.cam.2024.116452_b38) 2023; 88 Liu (10.1016/j.cam.2024.116452_b12) 2023; 94 Yuan (10.1016/j.cam.2024.116452_b53) 2019; 2 Wan (10.1016/j.cam.2024.116452_b21) 2011; 24 Sato (10.1016/j.cam.2024.116452_b41) 2021 Smith (10.1016/j.cam.2024.116452_b43) 1994; 3 10.1016/j.cam.2024.116452_b52 Jian (10.1016/j.cam.2024.116452_b16) 2015; 39 Zhu (10.1016/j.cam.2024.116452_b44) 2017; 67 Sakai (10.1016/j.cam.2024.116452_b29) 2020; 77 Townsend (10.1016/j.cam.2024.116452_b50) 2016; 17 Vandereycken (10.1016/j.cam.2024.116452_b51) 2013; 23 Liu (10.1016/j.cam.2024.116452_b17) 2024; 36 Tang (10.1016/j.cam.2024.116452_b45) 2023; 69 Zhang (10.1016/j.cam.2024.116452_b10) 2007; 22 Wu (10.1016/j.cam.2024.116452_b9) 2023; 422 Zoutendijk (10.1016/j.cam.2024.116452_b48) 1970 Dai (10.1016/j.cam.2024.116452_b6) 1999; 10 Hestenes (10.1016/j.cam.2024.116452_b2) 1952; 49 Jian (10.1016/j.cam.2024.116452_b24) 2022; 68 Crowder (10.1016/j.cam.2024.116452_b31) 1972; 16 Shao (10.1016/j.cam.2024.116452_b20) 2023; 118 Hu (10.1016/j.cam.2024.116452_b40) 2020; 8 Jiang (10.1016/j.cam.2024.116452_b7) 2021; 40 Polyak (10.1016/j.cam.2024.116452_b3) 1969; 9 Jian (10.1016/j.cam.2024.116452_b8) 2022; 48 Touati-Ahmed (10.1016/j.cam.2024.116452_b25) 1990; 64 Jian (10.1016/j.cam.2024.116452_b14) 2022; 68 Dai (10.1016/j.cam.2024.116452_b34) 2004; 35 Ring (10.1016/j.cam.2024.116452_b47) 2012; 22 Dolan (10.1016/j.cam.2024.116452_b49) 2002; 91 Andrei (10.1016/j.cam.2024.116452_b35) 2011; 34 Fletcher (10.1016/j.cam.2024.116452_b1) 1964; 7 Zhang (10.1016/j.cam.2024.116452_b28) 2008; 216 Liu (10.1016/j.cam.2024.116452_b22) 2019; 77 Sakai (10.1016/j.cam.2024.116452_b30) 2021; 190 Deng (10.1016/j.cam.2024.116452_b37) 2022; 43 Sato (10.1016/j.cam.2024.116452_b46) 2015; 64 Liu (10.1016/j.cam.2024.116452_b5) 1991; 69 Wang (10.1016/j.cam.2024.116452_b11) 2022; 93 Tian (10.1016/j.cam.2024.116452_b13) 2021; 9 Motzkin (10.1016/j.cam.2024.116452_b54) 1965; 17 Tang (10.1016/j.cam.2024.116452_b42) 2023; 94 Gilbert (10.1016/j.cam.2024.116452_b26) 1992; 2 Hu (10.1016/j.cam.2024.116452_b15) 1991; 71 Powell (10.1016/j.cam.2024.116452_b32) 1976; 11 Dai (10.1016/j.cam.2024.116452_b27) 2001; 103 Chen (10.1016/j.cam.2024.116452_b18) 2024; 204 Shao (10.1016/j.cam.2024.116452_b23) 2023; 118 Dai (10.1016/j.cam.2024.116452_b33) 1998; 41 Fletcher (10.1016/j.cam.2024.116452_b4) 1987 Jiang (10.1016/j.cam.2024.116452_b19) 2023; 38 Absil (10.1016/j.cam.2024.116452_b39) 2008 |
| References_xml | – volume: 69 start-page: 129 year: 1991 end-page: 137 ident: b5 article-title: Efficient generalized conjugate gradient algorithms, part 1: Theory publication-title: J. Optim. Theory Appl. – volume: 159 year: 2023 ident: b36 article-title: A family of hybrid conjugate gradient method with restart procedure for unconstrained optimizations and image restorations publication-title: Comput. Oper. Res. – volume: 68 start-page: 2407 year: 2022 end-page: 2433 ident: b14 article-title: A three-term conjugate gradient method with accelerated subspace quadratic optimization publication-title: J. Appl. Math. Comput. – year: 2008 ident: b39 article-title: Optimization Algorithms on Matrix Manifolds – year: 2021 ident: b41 article-title: Riemannian Optimization and Its Applications – year: 1987 ident: b4 article-title: Practical Methods of Optimization – volume: 39 start-page: 1281 year: 2015 end-page: 1290 ident: b16 article-title: A hybrid conjugate gradient method with descent property for unconstrained optimization publication-title: Appl. Math. Model. – volume: 118 start-page: 393 year: 2023 end-page: 411 ident: b23 article-title: Two families of self-adjusting spectral hybrid DL conjugate gradient methods and applications in image denoising publication-title: Applied Mathematical Modelling – volume: 11 start-page: 42 year: 1976 end-page: 49 ident: b32 article-title: Some convergence properties of the conjugate gradient method publication-title: Math. Program. – volume: 7 start-page: 149 year: 1964 end-page: 154 ident: b1 article-title: Function minimization by conjugate gradients publication-title: Comput. J. – volume: 36 start-page: 1445 year: 2024 end-page: 1463 ident: b17 article-title: Two efficient spectral hybrid cg methods based on memoryless BFGS direction and Dai–Liao conjugacy condition publication-title: Optimization Methods and Software – volume: 10 start-page: 177 year: 1999 end-page: 182 ident: b6 article-title: A nonlinear conjugate gradient method with a strong global convergence property publication-title: SIAM J. Optim. – volume: 3 start-page: 113 year: 1994 end-page: 135 ident: b43 article-title: Optimization techniques on Riemannian manifolds publication-title: Fields Inst. Commun. – reference: P.-A. Absil, K.A. Gallivan, Joint diagonalization on the oblique manifold for independent component analysis, in: 2006 IEEE International Conference on Acoustics, Speech and Signal Processing Proceedings, vol. 5, 2006, p. V. – volume: 88 start-page: 1 year: 2023 end-page: 32 ident: b38 article-title: Riemannian smoothing gradient type algorithms for nonsmooth optimization problem on compact Riemannian submanifold embedded in Euclidean space publication-title: Appl. Math. Optim. – volume: 8 start-page: 199 year: 2020 end-page: 248 ident: b40 article-title: A brief introduction to manifold optimization publication-title: J. Oper. Res. Soc. China – volume: 40 start-page: 174 year: 2021 ident: b7 article-title: An improved Polak-Ribière-Polyak conjugate gradient method with an efficient restart direction publication-title: Comput. Appl. Math. – volume: 94 start-page: 131 year: 2023 end-page: 147 ident: b42 article-title: A class of spectral conjugate gradient methods for Riemannian optimization publication-title: Numer. Algorithms – volume: 216 start-page: 251 year: 2008 end-page: 264 ident: b28 article-title: Two descent hybrid conjugate gradient methods for optimization publication-title: J. Comput. Appl. Math. – volume: 190 start-page: 130 year: 2021 end-page: 150 ident: b30 article-title: Sufficient descent Riemannian conjugate gradient methods publication-title: J. Optim. Theory Appl. – volume: 2 start-page: 1139 year: 2019 end-page: 1170 ident: b53 article-title: Global optimization with orthogonality constraints via stochastic diffusion on manifold publication-title: J. Sci. Comput. – volume: 43 start-page: 1653 year: 2022 end-page: 1684 ident: b37 article-title: A manifold inexact augmented Lagrangian method for nonsmooth optimization on Riemannian submanifolds in Euclidean space publication-title: IMA J. Numer. Anal. – volume: 35 start-page: 249 year: 2004 end-page: 260 ident: b34 article-title: On restart procedures for the conjugate gradient method publication-title: Numer. Algorithms – volume: 34 start-page: 319 year: 2011 end-page: 330 ident: b35 article-title: Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization publication-title: Bull. Malays. Math. Sci. Soc. (2) – volume: 71 start-page: 399 year: 1991 end-page: 405 ident: b15 article-title: Global convergence result for conjugate gradient methods publication-title: J. Optim. Theory Appl. – volume: 2 start-page: 21 year: 1992 end-page: 42 ident: b26 article-title: Global convergence properties of conjugate gradient methods for optimization publication-title: SIAM J. Optim. – volume: 16 start-page: 431 year: 1972 end-page: 433 ident: b31 article-title: Linear convergence of the conjugate gradient method publication-title: IBM J. Res. Dev. – volume: 118 start-page: 393 year: 2023 end-page: 411 ident: b20 article-title: Two families of self-adjusting spectral hybrid DL conjugate gradient methods and applications in image denoising publication-title: Appl. Math. Model. – volume: 204 start-page: 362 year: 2024 end-page: 379 ident: b18 article-title: An efficient hybrid conjugate gradient method with an adaptive strategy and applications in image restoration problems publication-title: Applied Numerical Mathematics – volume: 77 start-page: 811 year: 2020 end-page: 830 ident: b29 article-title: Hybrid Riemannian conjugate gradient methods with global convergence properties publication-title: Comput. Optim. Appl. – volume: 103 start-page: 33 year: 2001 end-page: 47 ident: b27 article-title: An efficient hybrid conjugate gradient method for unconstrained optimization publication-title: Ann. Oper. Res. – volume: 49 year: 1952 ident: b2 article-title: Methods of conjugate gradients for solving linear systems publication-title: J. Res. Natl. Bur. Stand. – volume: 422 year: 2023 ident: b9 article-title: An efficient conjugate gradient-based algorithm for unconstrained optimization and its projection extension to large-scale constrained nonlinear equations with application in signal recovery and image denoising problems publication-title: J. Comput. Appl. Math. – volume: 38 start-page: 947 year: 2023 end-page: 974 ident: b19 article-title: Two families of hybrid conjugate gradient methods with restart procedures and their applications publication-title: Optim. Methods Softw. – start-page: 37 year: 1970 end-page: 86 ident: b48 article-title: Nonlinear programming, computational methods publication-title: Int. Nonlinear Program. – volume: 91 start-page: 201 year: 2002 end-page: 213 ident: b49 article-title: Benchmarking optimization software with performance profiles publication-title: Math. Program. – volume: 69 start-page: 823 year: 2023 end-page: 852 ident: b45 article-title: A hybrid Riemannian conjugate gradient method for nonconvex optimization problems publication-title: J. Appl. Math. Comput. – volume: 41 start-page: 1142 year: 1998 end-page: 1150 ident: b33 article-title: Convergence properties of Beale-Powell restart algorithm publication-title: Sci. China Math. – volume: 17 start-page: 1 year: 2016 end-page: 5 ident: b50 article-title: Pymanopt: A Python toolbox for optimization on manifolds using automatic differentiation publication-title: J. Mach. Learn. Res. – volume: 22 start-page: 697 year: 2007 end-page: 711 ident: b10 article-title: Some descent three-term conjugate gradient methods and their global convergence publication-title: Optim. Methods Softw. – volume: 9 start-page: 94 year: 1969 end-page: 112 ident: b3 article-title: The conjugate gradient method in extremal problems publication-title: USSR Comput. Math. Math. Phys. – volume: 93 start-page: 949 year: 2022 end-page: 970 ident: b11 article-title: A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems publication-title: Numer. Algorithms – volume: 64 start-page: 379 year: 1990 end-page: 397 ident: b25 article-title: Efficient hybrid conjugate gradient techniques publication-title: J. Optim. Theory Appl. – volume: 23 start-page: 1214 year: 2013 end-page: 1236 ident: b51 article-title: Low-rank matrix completion by Riemannian optimization publication-title: SIAM J. Optim. – volume: 64 start-page: 1011 year: 2015 end-page: 1031 ident: b46 article-title: A new, globally convergent Riemannian conjugate gradient method publication-title: Optimization – volume: 48 start-page: 2297 year: 2022 end-page: 2319 ident: b8 article-title: Two improved nonlinear conjugate gradient methods with the strong wolfe line search publication-title: Bull. Iran. Math. Soc. – volume: 17 start-page: 533 year: 1965 end-page: 540 ident: b54 article-title: Maxima for graphs and a new proof of a theorem of Turán publication-title: Canad. J. Math. – volume: 9 year: 2021 ident: b13 article-title: A new hybrid three-term conjugate gradient algorithm for large-scale unconstrained problems publication-title: Mathematics – volume: 68 start-page: 4435 year: 2022 end-page: 4456 ident: b24 article-title: Two classes of spectral conjugate gradient methods for unconstrained optimizations publication-title: J. Appl. Math. Comput. – volume: 94 start-page: 1055 year: 2023 end-page: 1083 ident: b12 article-title: A family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial extensions for the constrained nonlinear pseudo-monotone equations with applications publication-title: Numer. Algorithms – volume: 77 start-page: 731 year: 2019 end-page: 739 ident: b22 article-title: A spectral conjugate gradient method for solving large-scale unconstrained optimization publication-title: Comput. Math. Appl. – volume: 22 start-page: 596 year: 2012 end-page: 627 ident: b47 article-title: Optimization methods on Riemannian manifolds and their application to shape space publication-title: SIAM J. Optim. – volume: 24 start-page: 16 year: 2011 end-page: 22 ident: b21 article-title: New spectral PRP conjugate gradient method for unconstrained optimization publication-title: Appl. Math. Lett. – volume: 67 start-page: 73 year: 2017 end-page: 110 ident: b44 article-title: A Riemannian conjugate gradient method for optimization on the Stiefel manifold publication-title: Comput. Optim. Appl. – volume: 93 start-page: 949 year: 2022 ident: 10.1016/j.cam.2024.116452_b11 article-title: A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems publication-title: Numer. Algorithms doi: 10.1007/s11075-022-01448-y – volume: 118 start-page: 393 year: 2023 ident: 10.1016/j.cam.2024.116452_b23 article-title: Two families of self-adjusting spectral hybrid DL conjugate gradient methods and applications in image denoising publication-title: Applied Mathematical Modelling doi: 10.1016/j.apm.2023.01.018 – volume: 77 start-page: 811 issue: 3 year: 2020 ident: 10.1016/j.cam.2024.116452_b29 article-title: Hybrid Riemannian conjugate gradient methods with global convergence properties publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-020-00224-9 – volume: 39 start-page: 1281 issue: 3–4 year: 2015 ident: 10.1016/j.cam.2024.116452_b16 article-title: A hybrid conjugate gradient method with descent property for unconstrained optimization publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2014.08.008 – volume: 24 start-page: 16 issue: 1 year: 2011 ident: 10.1016/j.cam.2024.116452_b21 article-title: New spectral PRP conjugate gradient method for unconstrained optimization publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2010.08.002 – volume: 23 start-page: 1214 issue: 2 year: 2013 ident: 10.1016/j.cam.2024.116452_b51 article-title: Low-rank matrix completion by Riemannian optimization publication-title: SIAM J. Optim. doi: 10.1137/110845768 – volume: 7 start-page: 149 issue: 2 year: 1964 ident: 10.1016/j.cam.2024.116452_b1 article-title: Function minimization by conjugate gradients publication-title: Comput. J. doi: 10.1093/comjnl/7.2.149 – volume: 9 start-page: 94 issue: 4 year: 1969 ident: 10.1016/j.cam.2024.116452_b3 article-title: The conjugate gradient method in extremal problems publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(69)90035-4 – volume: 422 year: 2023 ident: 10.1016/j.cam.2024.116452_b9 article-title: An efficient conjugate gradient-based algorithm for unconstrained optimization and its projection extension to large-scale constrained nonlinear equations with application in signal recovery and image denoising problems publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2022.114879 – volume: 94 start-page: 1055 year: 2023 ident: 10.1016/j.cam.2024.116452_b12 article-title: A family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial extensions for the constrained nonlinear pseudo-monotone equations with applications publication-title: Numer. Algorithms doi: 10.1007/s11075-023-01527-8 – volume: 77 start-page: 731 issue: 3 year: 2019 ident: 10.1016/j.cam.2024.116452_b22 article-title: A spectral conjugate gradient method for solving large-scale unconstrained optimization publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2018.10.002 – volume: 11 start-page: 42 year: 1976 ident: 10.1016/j.cam.2024.116452_b32 article-title: Some convergence properties of the conjugate gradient method publication-title: Math. Program. doi: 10.1007/BF01580369 – volume: 22 start-page: 697 issue: 4 year: 2007 ident: 10.1016/j.cam.2024.116452_b10 article-title: Some descent three-term conjugate gradient methods and their global convergence publication-title: Optim. Methods Softw. doi: 10.1080/10556780701223293 – volume: 34 start-page: 319 issue: 2 year: 2011 ident: 10.1016/j.cam.2024.116452_b35 article-title: Open problems in nonlinear conjugate gradient algorithms for unconstrained optimization publication-title: Bull. Malays. Math. Sci. Soc. (2) – volume: 48 start-page: 2297 year: 2022 ident: 10.1016/j.cam.2024.116452_b8 article-title: Two improved nonlinear conjugate gradient methods with the strong wolfe line search publication-title: Bull. Iran. Math. Soc. doi: 10.1007/s41980-021-00647-y – year: 2008 ident: 10.1016/j.cam.2024.116452_b39 – volume: 22 start-page: 596 issue: 2 year: 2012 ident: 10.1016/j.cam.2024.116452_b47 article-title: Optimization methods on Riemannian manifolds and their application to shape space publication-title: SIAM J. Optim. doi: 10.1137/11082885X – volume: 17 start-page: 1 issue: 137 year: 2016 ident: 10.1016/j.cam.2024.116452_b50 article-title: Pymanopt: A Python toolbox for optimization on manifolds using automatic differentiation publication-title: J. Mach. Learn. Res. – ident: 10.1016/j.cam.2024.116452_b52 doi: 10.1109/ICASSP.2006.1661433 – volume: 159 year: 2023 ident: 10.1016/j.cam.2024.116452_b36 article-title: A family of hybrid conjugate gradient method with restart procedure for unconstrained optimizations and image restorations publication-title: Comput. Oper. Res. doi: 10.1016/j.cor.2023.106341 – volume: 43 start-page: 1653 issue: 3 year: 2022 ident: 10.1016/j.cam.2024.116452_b37 article-title: A manifold inexact augmented Lagrangian method for nonsmooth optimization on Riemannian submanifolds in Euclidean space publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drac018 – volume: 38 start-page: 947 issue: 5 year: 2023 ident: 10.1016/j.cam.2024.116452_b19 article-title: Two families of hybrid conjugate gradient methods with restart procedures and their applications publication-title: Optim. Methods Softw. doi: 10.1080/10556788.2023.2189718 – volume: 216 start-page: 251 issue: 1 year: 2008 ident: 10.1016/j.cam.2024.116452_b28 article-title: Two descent hybrid conjugate gradient methods for optimization publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.04.028 – volume: 8 start-page: 199 year: 2020 ident: 10.1016/j.cam.2024.116452_b40 article-title: A brief introduction to manifold optimization publication-title: J. Oper. Res. Soc. China doi: 10.1007/s40305-020-00295-9 – volume: 35 start-page: 249 year: 2004 ident: 10.1016/j.cam.2024.116452_b34 article-title: On restart procedures for the conjugate gradient method publication-title: Numer. Algorithms doi: 10.1023/B:NUMA.0000021761.10993.6e – volume: 69 start-page: 823 issue: 1 year: 2023 ident: 10.1016/j.cam.2024.116452_b45 article-title: A hybrid Riemannian conjugate gradient method for nonconvex optimization problems publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-022-01772-5 – volume: 2 start-page: 21 issue: 1 year: 1992 ident: 10.1016/j.cam.2024.116452_b26 article-title: Global convergence properties of conjugate gradient methods for optimization publication-title: SIAM J. Optim. doi: 10.1137/0802003 – volume: 64 start-page: 379 year: 1990 ident: 10.1016/j.cam.2024.116452_b25 article-title: Efficient hybrid conjugate gradient techniques publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00939455 – volume: 36 start-page: 1445 issue: 6 year: 2024 ident: 10.1016/j.cam.2024.116452_b17 article-title: Two efficient spectral hybrid cg methods based on memoryless BFGS direction and Dai–Liao conjugacy condition publication-title: Optimization Methods and Software doi: 10.1080/10556788.2024.2364203 – volume: 10 start-page: 177 issue: 1 year: 1999 ident: 10.1016/j.cam.2024.116452_b6 article-title: A nonlinear conjugate gradient method with a strong global convergence property publication-title: SIAM J. Optim. doi: 10.1137/S1052623497318992 – volume: 9 issue: 12 year: 2021 ident: 10.1016/j.cam.2024.116452_b13 article-title: A new hybrid three-term conjugate gradient algorithm for large-scale unconstrained problems publication-title: Mathematics doi: 10.3390/math9121353 – volume: 17 start-page: 533 year: 1965 ident: 10.1016/j.cam.2024.116452_b54 article-title: Maxima for graphs and a new proof of a theorem of Turán publication-title: Canad. J. Math. doi: 10.4153/CJM-1965-053-6 – year: 1987 ident: 10.1016/j.cam.2024.116452_b4 – year: 2021 ident: 10.1016/j.cam.2024.116452_b41 – volume: 2 start-page: 1139 issue: 80 year: 2019 ident: 10.1016/j.cam.2024.116452_b53 article-title: Global optimization with orthogonality constraints via stochastic diffusion on manifold publication-title: J. Sci. Comput. doi: 10.1007/s10915-019-00971-w – volume: 68 start-page: 4435 issue: 6 year: 2022 ident: 10.1016/j.cam.2024.116452_b24 article-title: Two classes of spectral conjugate gradient methods for unconstrained optimizations publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-022-01713-2 – volume: 68 start-page: 2407 year: 2022 ident: 10.1016/j.cam.2024.116452_b14 article-title: A three-term conjugate gradient method with accelerated subspace quadratic optimization publication-title: J. Appl. Math. Comput. doi: 10.1007/s12190-021-01622-w – volume: 16 start-page: 431 issue: 4 year: 1972 ident: 10.1016/j.cam.2024.116452_b31 article-title: Linear convergence of the conjugate gradient method publication-title: IBM J. Res. Dev. doi: 10.1147/rd.164.0431 – volume: 91 start-page: 201 year: 2002 ident: 10.1016/j.cam.2024.116452_b49 article-title: Benchmarking optimization software with performance profiles publication-title: Math. Program. doi: 10.1007/s101070100263 – volume: 69 start-page: 129 year: 1991 ident: 10.1016/j.cam.2024.116452_b5 article-title: Efficient generalized conjugate gradient algorithms, part 1: Theory publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00940464 – volume: 41 start-page: 1142 year: 1998 ident: 10.1016/j.cam.2024.116452_b33 article-title: Convergence properties of Beale-Powell restart algorithm publication-title: Sci. China Math. doi: 10.1007/BF02871976 – volume: 3 start-page: 113 issue: 3 year: 1994 ident: 10.1016/j.cam.2024.116452_b43 article-title: Optimization techniques on Riemannian manifolds publication-title: Fields Inst. Commun. – volume: 88 start-page: 1 issue: 85 year: 2023 ident: 10.1016/j.cam.2024.116452_b38 article-title: Riemannian smoothing gradient type algorithms for nonsmooth optimization problem on compact Riemannian submanifold embedded in Euclidean space publication-title: Appl. Math. Optim. – volume: 118 start-page: 393 year: 2023 ident: 10.1016/j.cam.2024.116452_b20 article-title: Two families of self-adjusting spectral hybrid DL conjugate gradient methods and applications in image denoising publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2023.01.018 – volume: 64 start-page: 1011 issue: 4 year: 2015 ident: 10.1016/j.cam.2024.116452_b46 article-title: A new, globally convergent Riemannian conjugate gradient method publication-title: Optimization doi: 10.1080/02331934.2013.836650 – volume: 49 issue: 6 year: 1952 ident: 10.1016/j.cam.2024.116452_b2 article-title: Methods of conjugate gradients for solving linear systems publication-title: J. Res. Natl. Bur. Stand. doi: 10.6028/jres.049.044 – volume: 204 start-page: 362 year: 2024 ident: 10.1016/j.cam.2024.116452_b18 article-title: An efficient hybrid conjugate gradient method with an adaptive strategy and applications in image restoration problems publication-title: Applied Numerical Mathematics doi: 10.1016/j.apnum.2024.06.020 – volume: 67 start-page: 73 year: 2017 ident: 10.1016/j.cam.2024.116452_b44 article-title: A Riemannian conjugate gradient method for optimization on the Stiefel manifold publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-016-9883-4 – volume: 71 start-page: 399 year: 1991 ident: 10.1016/j.cam.2024.116452_b15 article-title: Global convergence result for conjugate gradient methods publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00939927 – volume: 94 start-page: 131 year: 2023 ident: 10.1016/j.cam.2024.116452_b42 article-title: A class of spectral conjugate gradient methods for Riemannian optimization publication-title: Numer. Algorithms doi: 10.1007/s11075-022-01495-5 – volume: 190 start-page: 130 issue: 1 year: 2021 ident: 10.1016/j.cam.2024.116452_b30 article-title: Sufficient descent Riemannian conjugate gradient methods publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-021-01874-3 – start-page: 37 year: 1970 ident: 10.1016/j.cam.2024.116452_b48 article-title: Nonlinear programming, computational methods publication-title: Int. Nonlinear Program. – volume: 103 start-page: 33 year: 2001 ident: 10.1016/j.cam.2024.116452_b27 article-title: An efficient hybrid conjugate gradient method for unconstrained optimization publication-title: Ann. Oper. Res. doi: 10.1023/A:1012930416777 – volume: 40 start-page: 174 issue: 5 year: 2021 ident: 10.1016/j.cam.2024.116452_b7 article-title: An improved Polak-Ribière-Polyak conjugate gradient method with an efficient restart direction publication-title: Comput. Appl. Math. doi: 10.1007/s40314-021-01557-9 |
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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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