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A modified descent Polak–Ribiére–Polyak conjugate gradient method with global convergence property for nonconvex functions

Abstract

Following the modification scheme of Dong et al. made on the Hestenes–Stiefel method, we suggest a modified Polak–Ribiére–Polyak technique which satisfies the sufficient descent condition. We show that the method is globally convergent with the Wolfe line search conditions as well as the backtracking Armijo-type line search strategy proposed by Grippo and Lucidi, without convexity assumption on the objective function. Numerical experiments on some test functions of the CUTEr collection show that the method performs promisingly.

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Acknowledgements

This research was in part supported by the grant 97022259 from Iran National Science Foundation (INSF), and in part by the Research Council of Semnan University. The authors thank the anonymous reviewers for their valuable comments and suggestions helped to improve the quality of this work. They are also grateful to Professor Michael Navon for providing the line search code.

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Correspondence to Saman Babaie-Kafaki.

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Aminifard, Z., Babaie-Kafaki, S. A modified descent Polak–Ribiére–Polyak conjugate gradient method with global convergence property for nonconvex functions. Calcolo 56, 16 (2019). https://doi.org/10.1007/s10092-019-0312-9

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Keywords

  • Unconstrained optimization
  • Conjugate gradient method
  • Sufficient descent condition
  • Line search
  • Global convergence

Mathematics Subject Classification

  • 90C53
  • 65K05