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Open AccessArticle

A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems

School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China
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Algorithms 2018, 11(9), 133; https://doi.org/10.3390/a11090133
Received: 4 July 2018 / Revised: 24 August 2018 / Accepted: 3 September 2018 / Published: 6 September 2018
In this paper, a modification to the Polak–Ribiére–Polyak (PRP) nonlinear conjugate gradient method is presented. The proposed method always generates a sufficient descent direction independent of the accuracy of the line search and the convexity of the objective function. Under appropriate conditions, the modified method is proved to possess global convergence under the Wolfe or Armijo-type line search. Moreover, the proposed methodology is adopted in the Hestenes–Stiefel (HS) and Liu–Storey (LS) methods. Extensive preliminary numerical experiments are used to illustrate the efficiency of the proposed method. View Full-Text
Keywords: unconstrained optimization; conjugate gradient method; sufficient descent; global convergence unconstrained optimization; conjugate gradient method; sufficient descent; global convergence
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MDPI and ACS Style

Zheng, X.; Shi, J. A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems. Algorithms 2018, 11, 133. https://doi.org/10.3390/a11090133

AMA Style

Zheng X, Shi J. A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems. Algorithms. 2018; 11(9):133. https://doi.org/10.3390/a11090133

Chicago/Turabian Style

Zheng, Xiuyun; Shi, Jiarong. 2018. "A Modified Sufficient Descent Polak–Ribiére–Polyak Type Conjugate Gradient Method for Unconstrained Optimization Problems" Algorithms 11, no. 9: 133. https://doi.org/10.3390/a11090133

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