A new family of hybrid three-term conjugate gradient methods with applications in image restoration

In this paper, based on the hybrid conjugate gradient method and the convex combination technique, a new family of hybrid three-term conjugate gradient methods are proposed for solving unconstrained optimization. The conjugate parameter in the search direction is a hybrid of Dai-Yuan conjugate param...

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Vydáno v:	Numerical algorithms Ročník 91; číslo 1; s. 161 - 191
Hlavní autoři:	Jiang, Xianzhen, Liao, Wei, Yin, Jianghua, Jian, Jinbao
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.09.2022 Springer Nature B.V
Témata:	Algebra Algorithms Computer Science Conjugate gradient method Design Design parameters Hypotheses Image restoration Iterative methods Numeric Computing Numerical Analysis Optimization Original Paper Searching Theory of Computation Descent property 68U10 Global convergence Unconstrained optimization Hybrid three-term conjugate gradient method 65K10 Image restoration 49M37
ISSN:	1017-1398, 1572-9265
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Abstract	In this paper, based on the hybrid conjugate gradient method and the convex combination technique, a new family of hybrid three-term conjugate gradient methods are proposed for solving unconstrained optimization. The conjugate parameter in the search direction is a hybrid of Dai-Yuan conjugate parameter and any one. The search direction then is the sum of the negative gradient direction and a convex combination in relation to the last search direction and the gradient at the previous iteration. Without choosing any specific conjugate parameters, we show that the search direction generated by the family always possesses the descent property independent of line search technique, and that it is globally convergent under usual assumptions and the weak Wolfe line search. To verify the effectiveness of the presented family, we further design a specific conjugate parameter, and perform medium-large-scale numerical experiments for smooth unconstrained optimization and image restoration problems. The numerical results show the encouraging efficiency and applicability of the proposed methods even compared with the state-of-the-art methods.
AbstractList	In this paper, based on the hybrid conjugate gradient method and the convex combination technique, a new family of hybrid three-term conjugate gradient methods are proposed for solving unconstrained optimization. The conjugate parameter in the search direction is a hybrid of Dai-Yuan conjugate parameter and any one. The search direction then is the sum of the negative gradient direction and a convex combination in relation to the last search direction and the gradient at the previous iteration. Without choosing any specific conjugate parameters, we show that the search direction generated by the family always possesses the descent property independent of line search technique, and that it is globally convergent under usual assumptions and the weak Wolfe line search. To verify the effectiveness of the presented family, we further design a specific conjugate parameter, and perform medium-large-scale numerical experiments for smooth unconstrained optimization and image restoration problems. The numerical results show the encouraging efficiency and applicability of the proposed methods even compared with the state-of-the-art methods.
Author	Liao, Wei Yin, Jianghua Jian, Jinbao Jiang, Xianzhen
Author_xml	– sequence: 1 givenname: Xianzhen surname: Jiang fullname: Jiang, Xianzhen organization: College of Mathematics and Physics, Guangxi University for Nationalities – sequence: 2 givenname: Wei surname: Liao fullname: Liao, Wei organization: College of Mathematics and Physics, Guangxi University for Nationalities – sequence: 3 givenname: Jianghua surname: Yin fullname: Yin, Jianghua organization: College of Mathematics and Physics, Guangxi University for Nationalities – sequence: 4 givenname: Jinbao orcidid: 0000-0001-8048-7397 surname: Jian fullname: Jian, Jinbao email: jianjb@gxu.edu.cn organization: College of Mathematics and Physics, Guangxi University for Nationalities
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Snippet	In this paper, based on the hybrid conjugate gradient method and the convex combination technique, a new family of hybrid three-term conjugate gradient methods...
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SubjectTerms	Algebra Algorithms Computer Science Conjugate gradient method Design Design parameters Hypotheses Image restoration Iterative methods Numeric Computing Numerical Analysis Optimization Original Paper Searching Theory of Computation
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Title	A new family of hybrid three-term conjugate gradient methods with applications in image restoration
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