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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Published in:Computational optimization and applications Vol. 75; no. 1; pp. 145 - 167
Main Authors: Liu, Zexian, Liu, Hongwei, Dai, Yu-Hong
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2020
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-019-00143-4