A Convex Combination between Two Different Search Directions of Conjugate Gradient Method and Application in Image Restoration | Zendy

Ahmad Alhawarat | Zendy; Zabidin Salleh | Zendy; Ibtisam Masmali | Zendy

Open Access

A Convex Combination between Two Different Search Directions of Conjugate Gradient Method and Application in Image Restoration

Author(s) -

Ahmad Alhawarat,

Zabidin Salleh,

Ibtisam Masmali

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/9941757

Subject(s) - conjugate gradient method , derivation of the conjugate gradient method , conjugate residual method , gradient descent , nonlinear conjugate gradient method , mathematics , convergence (economics) , biconjugate gradient method , gradient method , proximal gradient methods , conjugate , regular polygon , mathematical optimization , stochastic gradient descent , convex function , algorithm , computer science , mathematical analysis , geometry , artificial intelligence , artificial neural network , economics , economic growth

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.

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