### Journals Information

Mathematics and Statistics Vol. 10(2), pp. 293 - 300
DOI: 10.13189/ms.2022.100202
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## A New Algorithm for Spectral Conjugate Gradient in Nonlinear Optimization

Ahmed Anwer Mustafa *
Department of Mathematics, Faculty of Education, University of Zakho, Kurdistan Region, Iraq

ABSTRACT

CJG is a nonlinear conjugation gradient. Algorithms have been used to solve large-scale unconstrained enhancement problems. Because of their minimal memory needs and global convergence qualities, they are widely used in a variety of fields. This approach has lately undergone many investigations and modifications to enhance it. In our daily lives, the conjugate gradient is incredibly significant. For example, whatever we do, we strive for the best outcomes, such as the highest profit, the lowest loss, the shortest road, or the shortest time, which are referred to as the minimum and maximum in mathematics, and one of these ways is the process of spectral gradient descent. For multidimensional unbounded objective function, the spectrum conjugated gradient (SCJG) approach is a strong tool. In this study, we describe a revolutionary SCG technique in which performance is quantified. Based on assumptions, we constructed the descent condition, sufficient descent theorem, conjugacy condition, and global convergence criteria using a robust Wolfe and Powell line search. Numerical data and graphs were constructed utilizing benchmark functions, which are often used in many classical functions, to demonstrate the efficacy of the recommended approach. According to numerical statistics, the suggested strategy is more efficient than some current techniques. In addition, we show how the unique method may be utilized to improve solutions and outcomes.

KEYWORDS
New Spectral Conjugated Gradient, Optimization with No Constraints, Analytical Convergence, Conjugacy Requirement, Sufficient Descent Inequality

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ahmed Anwer Mustafa , "A New Algorithm for Spectral Conjugate Gradient in Nonlinear Optimization," Mathematics and Statistics, Vol. 10, No. 2, pp. 293 - 300, 2022. DOI: 10.13189/ms.2022.100202.

(b). APA Format:
Ahmed Anwer Mustafa (2022). A New Algorithm for Spectral Conjugate Gradient in Nonlinear Optimization. Mathematics and Statistics, 10(2), 293 - 300. DOI: 10.13189/ms.2022.100202.