An improved Dai–Kou conjugate gradient algorithm for unconstrained optimization

Zexian Liu (), Hongwei Liu () and Yu-Hong Dai ()
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Zexian Liu: Xidian University
Hongwei Liu: Xidian University
Yu-Hong Dai: Chinese Academy of Sciences

Computational Optimization and Applications, 2020, vol. 75, issue 1, No 6, 145-167

Abstract: 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.

Keywords: Conjugate gradient algorithm; Limited memory; Quasi-Newton method; Preconditioned conjugate gradient algorithm; Global convergence; 90C06; 90C26; 65Y20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10589-019-00143-4

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