Multi-step nonlinear conjugate gradient methods for unconstrained minimization |
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Authors: | John A Ford Yasushi Narushima Hiroshi Yabe |
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Institution: | (1) Department of Computer Science, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, UK;(2) Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan |
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Abstract: | Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of
matrices. Recently, seeking fast convergence of these methods, Dai and Liao (Appl. Math. Optim. 43:87–101, 2001) proposed a conjugate gradient method based on the secant condition of quasi-Newton methods, and later Yabe and Takano (Comput.
Optim. Appl. 28:203–225, 2004) proposed another conjugate gradient method based on the modified secant condition. In this paper, we make use of a multi-step
secant condition given by Ford and Moghrabi (Optim. Methods Softw. 2:357–370, 1993; J. Comput. Appl. Math. 50:305–323, 1994) and propose two new conjugate gradient methods based on this condition. The methods are shown to be globally convergent
under certain assumptions. Numerical results are reported. |
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Keywords: | Unconstrained optimization Conjugate gradient method Line search Global convergence Multi-step secant condition |
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