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A family of hybrid conjugate gradient methods for unconstrained optimization

Author: Yu-Hong Dai
Journal: Math. Comp. 72 (2003), 1317-1328
MSC (2000): Primary 49M37, 65K05, 90C30
Published electronically: February 3, 2003
MathSciNet review: 1972738
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Abstract: Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. This paper proposes a three-parameter family of hybrid conjugate gradient methods. Two important features of the family are that (i) it can avoid the propensity of small steps, namely, if a small step is generated away from the solution point, the next search direction will be close to the negative gradient direction; and (ii) its descent property and global convergence are likely to be achieved provided that the line search satisfies the Wolfe conditions. Some numerical results with the family are also presented.

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Additional Information

Yu-Hong Dai
Affiliation: State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P. O. Box 2719, Beijing 100080, Peoples Republic of China

Keywords: Unconstrained optimization, conjugate gradient method, line search, descent property, global convergence
Received by editor(s): May 19, 2000
Received by editor(s) in revised form: November 9, 2001
Published electronically: February 3, 2003
Additional Notes: Research partly supported by the Chinese NSF grants 19801033, 10171104 and a Youth Innovation Fund of the Chinese Academy of Sciences
Article copyright: © Copyright 2003 American Mathematical Society