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A modified Polak–Ribière–Polyak conjugate gradient algorithm for large-scale optimization problems

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  • Gonglin Yuan
  • Zengxin Wei
  • Qiumei Zhao

Abstract

Mathematical programming is a rich and well-advanced area in operations research. However, there are still many challenging problems in mathematical programming, and the large-scale optimization problem is one of them. In this article, a modified Polak–Ribière–Polyak conjugate gradient algorithm that incorporates a non-monotone line search technique is presented. This method possesses not only gradient value information but also function value information. Moreover, the sufficient descent condition holds without any line search. Under suitable conditions, the global convergence is established for non-convex functions. Numerical results show that the proposed method is competitive with other conjugate gradient methods for large-scale optimization problems.

Suggested Citation

  • Gonglin Yuan & Zengxin Wei & Qiumei Zhao, 2014. "A modified Polak–Ribière–Polyak conjugate gradient algorithm for large-scale optimization problems," IISE Transactions, Taylor & Francis Journals, vol. 46(4), pages 397-413.
    • Handle: RePEc:taf:uiiexx:v:46:y:2014:i:4:p:397-413
    DOI: 10.1080/0740817X.2012.726757
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    Cited by:

    1. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    2. Gonglin Yuan & Xiabin Duan & Wenjie Liu & Xiaoliang Wang & Zengru Cui & Zhou Sheng, 2015. "Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-24, October.
    3. Xiaoliang Wang & Liping Pang & Qi Wu & Mingkun Zhang, 2021. "An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization," Mathematics, MDPI, vol. 9(8), pages 1-27, April.

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