A New Hybrid Descent Algorithm for Large-Scale Nonconvex Optimization and Application to Some Image Restoration Problems

Shuai Wang, Xiaoliang Wang (), Yuzhu Tian and Liping Pang
Additional contact information
Shuai Wang: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Xiaoliang Wang: Department of Mathematics and Science, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
Yuzhu Tian: School of Mathematics, Liaoning Normal University, Dalian 116026, China
Liping Pang: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Mathematics, 2024, vol. 12, issue 19, 1-16

Abstract: Conjugate gradient methods are widely used and attractive for large-scale unconstrained smooth optimization problems, with simple computation, low memory requirements, and interesting theoretical information on the features of curvature. Based on the strongly convergent property of the Dai–Yuan method and attractive numerical performance of the Hestenes–Stiefel method, a new hybrid descent conjugate gradient method is proposed in this paper. The proposed method satisfies the sufficient descent property independent of the accuracy of the line search strategies. Under the standard conditions, the trust region property and the global convergence are established, respectively. Numerical results of 61 problems with 9 large-scale dimensions and 46 ill-conditioned matrix problems reveal that the proposed method is more effective, robust, and reliable than the other methods. Additionally, the hybrid method also demonstrates reliable results for some image restoration problems.

Keywords: hybrid conjugate gradient method; acceleration scheme; sufficient descent property; global convergence; ill-conditioned matrix; image restoration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/19/3088/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/19/3088/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:19:p:3088-:d:1491128

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().