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A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration
Applications of Mathematics, Tome 69 (2024) no. 4, pp. 481-499 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2024.0009-24
Classification : 35Qxx, 47N10, 49M41, 49Q15
Keywords: unconstrained optimization; decreasing feature; global convergence; image restoration; conjugate gradient technique 
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     title = {A modified {Fletcher-Reeves} conjugate gradient method for unconstrained optimization with applications in image restoration},
     journal = {Applications of Mathematics},
     pages = {481--499},
     year = {2024},
     volume = {69},
     number = {4},
     doi = {10.21136/AM.2024.0009-24},
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2024.0009-24/}
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Ahmed, Zainab Hassan; Hbaib, Mohamed; Abbo, Khalil K. A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration. Applications of Mathematics, Tome 69 (2024) no. 4, pp. 481-499. doi: 10.21136/AM.2024.0009-24

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