A Hybrid Conjugate Gradient Algorithm for Nonconvex Functions and Its Applications in Image Restoration Problems

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  • College of Mathematics and Information Science, Center for Applied Mathematics of Guangxi, Guangxi University, Nanning, 530004, China

Received date: 2021-04-08

  Revised date: 2022-02-25

  Online published: 2023-12-26

Supported by

This work was supported by the National Natural Science Foundation of China (No. 11661009), the High Level Innovation Teams and Excellent Scholars Program in Guangxi institutions of higher education (No. [2019]52), the Guangxi Natural Science Key Fund (No. 2017GXNSFDA198046), the Special Funds for Local Science and Technology Development Guided by the Central Government (No. ZY20198003), and the special foundation for Guangxi Ba Gui Scholars.

Abstract

It is prominent that conjugate gradient method is a high-efficient solution way for large-scale optimization problems. However, most of the conjugate gradient methods do not have sufficient descent property. In this paper, without any line search, the presented method can generate sufficient descent directions and trust region property. While use some suitable conditions, the global convergence of the method is established with Armijo line search. Moreover, we study the proposed method for solving nonsmooth problems and establish its global convergence. The experiments show that the presented method can be applied to solve smooth and nonsmooth unconstrained problems, image restoration problems and Muskingum model successfully.

Cite this article

Gong-Lin Yuan, Ying-Jie Zhou, Meng-Xiang Zhang . A Hybrid Conjugate Gradient Algorithm for Nonconvex Functions and Its Applications in Image Restoration Problems[J]. Journal of the Operations Research Society of China, 2023 , 11(4) : 759 -781 . DOI: 10.1007/s40305-022-00424-6

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