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A Nonmonotone Scaled Fletcher–Reeves Conjugate Gradient Method with Application in Image Reconstruction

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Abstract

In an effort to make modification on the classical Fletcher–Reeves method, Jiang and Jian suggested an efficient nonlinear conjugate gradient algorithm which possesses the sufficient descent property when the line search fulfills the strong Wolfe conditions. Here, we develop a scaled modified version of the method which satisfies the sufficient descent condition independent of the line search. Also, a nonmonotone backtracking Armijo-type line search is proposed under which the global convergence of the method is established without convexity assumption. Performance of the method is evaluated by computational experiments on a set of CUTEr test functions and also, on the image reconstruction as a case study. The results show numerical efficiency of the method.

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Acknowledgements

This work is based upon research funded by Iran National Science Foundation (INSF) under project No 4000309. The authors are grateful to Professor Michael Navon for providing the strong Wolfe line search code. They also thank the anonymous reviewers for their valuable comments that helped to improve the quality of this work.

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Authors and Affiliations

  1. Department of Mathematics, Semnan University, P.O. Box: 35195–363, Semnan, Iran

    Nasrin Mirhoseini, Saman Babaie-Kafaki & Zohre Aminifard

Authors
  1. Nasrin Mirhoseini
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  2. Saman Babaie-Kafaki
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  3. Zohre Aminifard
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Correspondence to Saman Babaie-Kafaki.

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Communicated by Anton Abdulbasah Kamil.

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Mirhoseini, N., Babaie-Kafaki, S. & Aminifard, Z. A Nonmonotone Scaled Fletcher–Reeves Conjugate Gradient Method with Application in Image Reconstruction. Bull. Malays. Math. Sci. Soc. 45, 2885–2904 (2022). https://doi.org/10.1007/s40840-022-01303-2

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  • DOI: https://doi.org/10.1007/s40840-022-01303-2

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