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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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 461; p. 116452
Main Authors: Jiang, Meixuan, Wang, Yun, Shao, Hu, Wu, Ting, Sun, Weiwei
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2025
Subjects:
Adaptive restart strategy
Global convergence
Hybrid conjugate gradient method
Riemannian optimization
Global convergence
Hybrid conjugate gradient method
Riemannian optimization
Adaptive restart strategy
ISSN:0377-0427
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Summary: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.
ISSN:0377-0427
DOI:10.1016/j.cam.2024.116452