An improved Dai–Kou conjugate gradient algorithm for unconstrained optimization

It is gradually accepted that the loss of orthogonality of the gradients in a conjugate gradient algorithm may decelerate the convergence rate to some extent. The Dai–Kou conjugate gradient algorithm (SIAM J Optim 23(1):296–320, 2013), called CGOPT, has attracted many researchers’ attentions due to...

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Veröffentlicht in:	Computational optimization and applications Jg. 75; H. 1; S. 145 - 167
Hauptverfasser:	Liu, Zexian, Liu, Hongwei, Dai, Yu-Hong
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.01.2020 Springer Nature B.V
Schlagworte:	Algorithms Conjugates Convergence Convex and Discrete Geometry Deceleration Design modifications Distributed processing Management Science Mathematics Mathematics and Statistics Multiprocessing Numerical methods Operations Research Operations Research/Decision Theory Optimization Orthogonality Quasi Newton methods Queuing theory Statistics Global convergence Quasi-Newton method Preconditioned conjugate gradient algorithm 90C06 90C26 65Y20 Limited memory Conjugate gradient algorithm
ISSN:	0926-6003, 1573-2894
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Abstract	It is gradually accepted that the loss of orthogonality of the gradients in a conjugate gradient algorithm may decelerate the convergence rate to some extent. The Dai–Kou conjugate gradient algorithm (SIAM J Optim 23(1):296–320, 2013), called CGOPT, has attracted many researchers’ attentions due to its numerical efficiency. In this paper, we present an improved Dai–Kou conjugate gradient algorithm for unconstrained optimization, which only consists of two kinds of iterations. In the improved Dai–Kou conjugate gradient algorithm, we develop a new quasi-Newton method to improve the orthogonality by solving the subproblem in the subspace and design a modified strategy for the choice of the initial stepsize for improving the numerical performance. The global convergence of the improved Dai–Kou conjugate gradient algorithm is established without the strict assumptions in the convergence analysis of other limited memory conjugate gradient methods. Some numerical results suggest that the improved Dai–Kou conjugate gradient algorithm (CGOPT (2.0)) yields a tremendous improvement over the original Dai–Kou CG algorithm (CGOPT (1.0)) and is slightly superior to the latest limited memory conjugate gradient software package CG _ DESCENT (6.8) developed by Hager and Zhang (SIAM J Optim 23(4):2150–2168, 2013) for the CUTEr library.
AbstractList	It is gradually accepted that the loss of orthogonality of the gradients in a conjugate gradient algorithm may decelerate the convergence rate to some extent. The Dai–Kou conjugate gradient algorithm (SIAM J Optim 23(1):296–320, 2013), called CGOPT, has attracted many researchers’ attentions due to its numerical efficiency. In this paper, we present an improved Dai–Kou conjugate gradient algorithm for unconstrained optimization, which only consists of two kinds of iterations. In the improved Dai–Kou conjugate gradient algorithm, we develop a new quasi-Newton method to improve the orthogonality by solving the subproblem in the subspace and design a modified strategy for the choice of the initial stepsize for improving the numerical performance. The global convergence of the improved Dai–Kou conjugate gradient algorithm is established without the strict assumptions in the convergence analysis of other limited memory conjugate gradient methods. Some numerical results suggest that the improved Dai–Kou conjugate gradient algorithm (CGOPT (2.0)) yields a tremendous improvement over the original Dai–Kou CG algorithm (CGOPT (1.0)) and is slightly superior to the latest limited memory conjugate gradient software package CG _ DESCENT (6.8) developed by Hager and Zhang (SIAM J Optim 23(4):2150–2168, 2013) for the CUTEr library. It is gradually accepted that the loss of orthogonality of the gradients in a conjugate gradient algorithm may decelerate the convergence rate to some extent. The Dai–Kou conjugate gradient algorithm (SIAM J Optim 23(1):296–320, 2013), called CGOPT, has attracted many researchers’ attentions due to its numerical efficiency. In this paper, we present an improved Dai–Kou conjugate gradient algorithm for unconstrained optimization, which only consists of two kinds of iterations. In the improved Dai–Kou conjugate gradient algorithm, we develop a new quasi-Newton method to improve the orthogonality by solving the subproblem in the subspace and design a modified strategy for the choice of the initial stepsize for improving the numerical performance. The global convergence of the improved Dai–Kou conjugate gradient algorithm is established without the strict assumptions in the convergence analysis of other limited memory conjugate gradient methods. Some numerical results suggest that the improved Dai–Kou conjugate gradient algorithm (CGOPT (2.0)) yields a tremendous improvement over the original Dai–Kou CG algorithm (CGOPT (1.0)) and is slightly superior to the latest limited memory conjugate gradient software package CG\[\_ \]DESCENT (6.8) developed by Hager and Zhang (SIAM J Optim 23(4):2150–2168, 2013) for the CUTEr library.
Author	Liu, Zexian Dai, Yu-Hong Liu, Hongwei
Author_xml	– sequence: 1 givenname: Zexian surname: Liu fullname: Liu, Zexian organization: School of Mathematics and Statistics, Xidian University, LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences – sequence: 2 givenname: Hongwei surname: Liu fullname: Liu, Hongwei organization: School of Mathematics and Statistics, Xidian University – sequence: 3 givenname: Yu-Hong surname: Dai fullname: Dai, Yu-Hong email: dyh@lsec.cc.ac.cn organization: LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
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CitedBy_id	crossref_primary_10_1007_s12190_024_02209_x crossref_primary_10_1002_ima_22848 crossref_primary_10_1007_s10957_023_02265_6 crossref_primary_10_1080_00207160_2025_2517879 crossref_primary_10_1007_s10957_023_02325_x crossref_primary_10_1080_10556788_2024_2329591 crossref_primary_10_1007_s40305_025_00593_0 crossref_primary_10_1007_s11075_024_01764_5 crossref_primary_10_1177_01423312231159216 crossref_primary_10_1016_j_matcom_2021_05_038 crossref_primary_10_1007_s11075_023_01559_0
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Snippet	It is gradually accepted that the loss of orthogonality of the gradients in a conjugate gradient algorithm may decelerate the convergence rate to some extent....
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SubjectTerms	Algorithms Conjugates Convergence Convex and Discrete Geometry Deceleration Design modifications Distributed processing Management Science Mathematics Mathematics and Statistics Multiprocessing Numerical methods Operations Research Operations Research/Decision Theory Optimization Orthogonality Quasi Newton methods Queuing theory Statistics
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Title	An improved Dai–Kou conjugate gradient algorithm for unconstrained optimization
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