A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration

Zainab Hassan Ahmed; Mohamed Hbaib; Khalil K. Abbo

Applications of Mathematics (2024)

  • Volume: 69, Issue: 4, page 481-499
  • ISSN: 0862-7940

Abstract

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The Fletcher-Reeves (FR) method is widely recognized for its drawbacks, such as generating unfavorable directions and taking small steps, which can lead to subsequent poor directions and steps. To address this issue, we propose a modification to the FR method, and then we develop it into the three-term conjugate gradient method in this paper. The suggested methods, named ``HZF'' and ``THZF'', preserve the descent property of the FR method while mitigating the drawbacks. The algorithms incorporate strong Wolfe line search conditions to ensure effective convergence. Through numerical comparisons with other conjugate gradient algorithms, our modified approach demonstrates superior performance. The results highlight the improved efficacy of the HZF algorithm compared to the FR and three-term FR conjugate gradient methods. The new algorithm was applied to the problem of image restoration and proved to be highly effective in image restoration compared to other algorithms.

How to cite

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Ahmed, Zainab Hassan, Hbaib, Mohamed, and Abbo, Khalil K.. "A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration." Applications of Mathematics 69.4 (2024): 481-499. <http://eudml.org/doc/299595>.

@article{Ahmed2024,
abstract = {The Fletcher-Reeves (FR) method is widely recognized for its drawbacks, such as generating unfavorable directions and taking small steps, which can lead to subsequent poor directions and steps. To address this issue, we propose a modification to the FR method, and then we develop it into the three-term conjugate gradient method in this paper. The suggested methods, named ``HZF'' and ``THZF'', preserve the descent property of the FR method while mitigating the drawbacks. The algorithms incorporate strong Wolfe line search conditions to ensure effective convergence. Through numerical comparisons with other conjugate gradient algorithms, our modified approach demonstrates superior performance. The results highlight the improved efficacy of the HZF algorithm compared to the FR and three-term FR conjugate gradient methods. The new algorithm was applied to the problem of image restoration and proved to be highly effective in image restoration compared to other algorithms.},
author = {Ahmed, Zainab Hassan, Hbaib, Mohamed, Abbo, Khalil K.},
journal = {Applications of Mathematics},
keywords = {unconstrained optimization; decreasing feature; global convergence; image restoration; conjugate gradient technique},
language = {eng},
number = {4},
pages = {481-499},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration},
url = {http://eudml.org/doc/299595},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Ahmed, Zainab Hassan
AU - Hbaib, Mohamed
AU - Abbo, Khalil K.
TI - A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 481
EP - 499
AB - The Fletcher-Reeves (FR) method is widely recognized for its drawbacks, such as generating unfavorable directions and taking small steps, which can lead to subsequent poor directions and steps. To address this issue, we propose a modification to the FR method, and then we develop it into the three-term conjugate gradient method in this paper. The suggested methods, named ``HZF'' and ``THZF'', preserve the descent property of the FR method while mitigating the drawbacks. The algorithms incorporate strong Wolfe line search conditions to ensure effective convergence. Through numerical comparisons with other conjugate gradient algorithms, our modified approach demonstrates superior performance. The results highlight the improved efficacy of the HZF algorithm compared to the FR and three-term FR conjugate gradient methods. The new algorithm was applied to the problem of image restoration and proved to be highly effective in image restoration compared to other algorithms.
LA - eng
KW - unconstrained optimization; decreasing feature; global convergence; image restoration; conjugate gradient technique
UR - http://eudml.org/doc/299595
ER -

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