TY - JOUR
T1 - Nonlinear conjugate gradient methods with sufficient descent properties for unconstrained optimization
AU - Nakamura, Wataru
AU - Narushima, Yasushi
AU - Yabe, Hiroshi
N1 - Funding Information:
The authors would like to thank the associate editor and the referees for their valuable comments. The second and third authors are supported in part by the Grant-in-Aid for Scientific Research (C) 25330030 of Japan Society for the Promotion of Science.
Publisher Copyright:
© 2013, American Institute of Mathematical Sciences.
PY - 2013
Y1 - 2013
N2 - It is very important to generate a descent search direction independent of line searches in showing the global convergence of conjugate gradient methods. The method of Hager and Zhang (2005) satisfies the sufficient descent condition. In this paper, we treat two subjects. We first consider a unified formula of parameters which establishes the sufficient descent condition and follows the modification technique of Hager and Zhang. In order to show the global convergence of the conjugate gradient method with the unified formula of parameters, we define some property (say Property A). We prove the global convergence of the method with Property A. Next, we apply the unified formula to a scaled conjugate gradient method and show its global convergence property. Finally numerical results are given.
AB - It is very important to generate a descent search direction independent of line searches in showing the global convergence of conjugate gradient methods. The method of Hager and Zhang (2005) satisfies the sufficient descent condition. In this paper, we treat two subjects. We first consider a unified formula of parameters which establishes the sufficient descent condition and follows the modification technique of Hager and Zhang. In order to show the global convergence of the conjugate gradient method with the unified formula of parameters, we define some property (say Property A). We prove the global convergence of the method with Property A. Next, we apply the unified formula to a scaled conjugate gradient method and show its global convergence property. Finally numerical results are given.
KW - Global convergence
KW - Nonlinear conjugate gradient method
KW - Scaled conjugate gradient method
KW - Sufficient descent property
KW - Unconstrained optimization
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U2 - 10.3934/jimo.2013.9.595
DO - 10.3934/jimo.2013.9.595
M3 - Article
AN - SCOPUS:84890017726
SN - 1547-5816
VL - 9
SP - 595
EP - 619
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
IS - 3
ER -