A Convex Combination between Two Different Search Directions of Conjugate Gradient Method and Application in Image Restoration. (13th July 2021)

• Record Type: Journal Article
• Authors: Alhawarat, Ahmad; Salleh, Zabidin; Masmali, Ibtisam A.
• Other Names: Jankowski Łukasz Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-07-13
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/9941757
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : The conjugate gradient is a useful tool in solving large- and small-scale unconstrained optimization problems. In addition, the conjugate gradient method can be applied in many fields, such as engineering, medical research, and computer science. In this paper, a convex combination of two different search directions is proposed. The new combination satisfies the sufficient descent condition and the convergence analysis. Moreover, a new conjugate gradient formula is proposed. The new formula satisfies the convergence properties with the descent property related to Hestenes–Stiefel conjugate gradient formula. The numerical results show that the new search direction outperforms both two search directions, making it convex between them. The numerical result includes the number of iterations, function evaluations, and central processing unit time. Finally, we present some examples about image restoration as an application of the proposed conjugate gradient method.