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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Veröffentlicht in:Numerical algorithms Jg. 91; H. 1; S. 161 - 191
Hauptverfasser: Jiang, Xianzhen, Liao, Wei, Yin, Jianghua, Jian, Jinbao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.09.2022
Springer Nature B.V
Schlagworte:
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
Online-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01258-2