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A descent extension of a modified Polak–Ribière–Polyak method with application in image restoration problem

A descent extension of a modified Polak–Ribière–Polyak method with application in image... A one-parameter extension of the modified Polak–Ribière–Polyak method proposed by Sun and Liu is developed based on the Dai–Liao approach. Two adaptive choices for the parameter of the method are suggested, one of which is obtained by carrying out an eigenvalue analysis, and the other is determined by minimizing the distance between search direction of the method and direction of the three-term conjugate gradient method proposed by Sun and Liu. It is shown that the method may satisfy the sufficient descent condition when its parameter is chosen appropriately. Global convergence analysis is conducted. At last, practical merits of the method are investigated by numerical experiments on a set of CUTEr test functions as well as the well-known image restoration problem. The results show numerical efficiency of the method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimization Letters Springer Journals

A descent extension of a modified Polak–Ribière–Polyak method with application in image restoration problem

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References (79)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022
ISSN
1862-4472
eISSN
1862-4480
DOI
10.1007/s11590-022-01878-6
Publisher site
See Article on Publisher Site

Abstract

A one-parameter extension of the modified Polak–Ribière–Polyak method proposed by Sun and Liu is developed based on the Dai–Liao approach. Two adaptive choices for the parameter of the method are suggested, one of which is obtained by carrying out an eigenvalue analysis, and the other is determined by minimizing the distance between search direction of the method and direction of the three-term conjugate gradient method proposed by Sun and Liu. It is shown that the method may satisfy the sufficient descent condition when its parameter is chosen appropriately. Global convergence analysis is conducted. At last, practical merits of the method are investigated by numerical experiments on a set of CUTEr test functions as well as the well-known image restoration problem. The results show numerical efficiency of the method.

Journal

Optimization LettersSpringer Journals

Published: Mar 1, 2023

Keywords: Unconstrained optimization; Conjugate gradient method; Eigenvalue; Descent condition; Image restoration

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