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Global convergence of the Polak-Ribière-Polyak conjugate gradient method with an Armijo-type inexact line search for nonconvex unconstrained optimization problems


Authors: Zeng Xin Wei, Guo Yin Li and Li Qun Qi
Journal: Math. Comp. 77 (2008), 2173-2193
MSC (2000): Primary 65H10, 90C26
Published electronically: June 11, 2008
MathSciNet review: 2429880
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Abstract | References | Similar Articles | Additional Information

Abstract: We propose two algorithms for nonconvex unconstrained optimization problems that employ Polak-Ribière-Polyak conjugate gradient formula and new inexact line search techniques. We show that the new algorithms converge globally if the function to be minimized has Lipschitz continuous gradients. Preliminary numerical results show that the proposed methods for particularly chosen line search conditions are very promising.


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Additional Information

Zeng Xin Wei
Affiliation: Department of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, People’s Republic of China
Email: zxwei@gxu.edu.cn

Guo Yin Li
Affiliation: Department of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, People’s Republic of China
Address at time of publication: Department of Applied Mathematics, The University of New South Wales, Australia
Email: g.li@unsw.edu.au

Li Qun Qi
Affiliation: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Email: maqilq@polyu.edu.hk

DOI: https://doi.org/10.1090/S0025-5718-08-02031-0
Keywords: Inexact line search, PRP method, nonconvex optimization, global convergence.
Received by editor(s): May 12, 2003
Received by editor(s) in revised form: June 12, 2004
Published electronically: June 11, 2008
Additional Notes: The first author’s work was done during his visit to the Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong and was supported by the Groucher Foundation of Hong Kong, Chinese NSF grant 10161002 and Guangxi NSF grant 0542043
The third author’s work was supported by the Research Grant Council of Hong Kong
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.