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New hybrid conjugate gradient method for nonlinear optimization with application to image restoration problems
Kybernetika, Tome 60 (2024) no. 4, pp. 535-552 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of $\beta _{k}^{RMIL}$ and $\beta _{k}^{HS}$. We compute the convex parameter $\theta _{k}$ using the Newton direction. Global convergence is established through the strong Wolfe conditions. Numerical experiments show the superior efficiency of our algorithm to solve unconstrained optimization problem compared to other considered methods. Applied to image restoration problem, our algorithm is competitive with existing algorithms and performs even better when the level of noise in the image is significant.
The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of $\beta _{k}^{RMIL}$ and $\beta _{k}^{HS}$. We compute the convex parameter $\theta _{k}$ using the Newton direction. Global convergence is established through the strong Wolfe conditions. Numerical experiments show the superior efficiency of our algorithm to solve unconstrained optimization problem compared to other considered methods. Applied to image restoration problem, our algorithm is competitive with existing algorithms and performs even better when the level of noise in the image is significant.
DOI : 10.14736/kyb-2024-4-0535
Classification : 65K05, 90C26, 90C30
Keywords: unconstrained optimization; conjugate gradient method; descent direction; line search; image restoration 
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     title = {New hybrid conjugate gradient method for nonlinear optimization with application to image restoration problems},
     journal = {Kybernetika},
     pages = {535--552},
     year = {2024},
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     number = {4},
     doi = {10.14736/kyb-2024-4-0535},
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     language = {en},
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Hemici, Youcef Elhamam; Khelladi, Samia; Benterki, Djamel. New hybrid conjugate gradient method for nonlinear optimization with application to image restoration problems. Kybernetika, Tome 60 (2024) no. 4, pp. 535-552. doi: 10.14736/kyb-2024-4-0535

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