A New Formula for Conjugate Gradient in Unconstrained Optimization
Article Sidebar
Main Article Content
Abstract
The method of Conjugate Gradient (CG) is a key component of optimization methods that aren't bound by local convergence characteristics. In this study, we created KHI3, a novel search direction in the (CG) Algorithm. The novel approach satisfies the regression criterion. The overall convergence of the proposed technique has also been proved utilizing Wolff search line words. A new algorithm for solving the large-scale unconstrained optimization issue is particularly successful.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
References
[1] D.F.J.M.o.o.r. Shanno, Conjugate gradient methods with inexact searches, Publisher, City, 1978.
[2] J. Barzilai, J.M. Borwein, Two-point step size gradient methods, Publisher, City, 1988.
[3] J.J.E. Dennis, J.J. Moré, Quasi-Newton Methods, Motivation and Theory, Publisher, City, 1977.
[4] Y.A. Laylani, K.K. Abbo, H.M. Khudhur, Training feed forward neural network with modified Fletcher-Reeves method, Publisher, City, 2018.
[5] R. Fletcher, C.M. Reeves, Function minimization by conjugate gradients, Publisher, City, 1964.
[6] Y.H. Dai, Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property, Publisher, City, 1999.
[7] R.J.J. Fletcher, C. Sons, Practical methods of optimization. 1987, Publisher, City, 1987.
[8] M.R. Hestenes, E. Stiefel, Methods of conjugate gradients for solving linear systems, Publisher, City, 1952.
[9] E. Polak, G. Ribiere, Note sur la convergence de méthodes de directions conjuguées, Publisher, City, 1969.
[10] Y. Liu, C. Storey, Efficient generalized conjugate gradient algorithms, part 1: Theory, Publisher, City, 1991.
[11] G.J.I. Zoutendijk, n. programming, Nonlinear programming, computational methods, Publisher, City, 1970.
[12] H.M. Khudhur, K.K. Abbo, A New Type of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Algebraic Equations, in: Journal of Physics: Conference Series, {IOP} Publishing, 2021.
[13] H.M. Khudhur, K.K. Abbo, New hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations, Publisher, City, 2021.
[14] W.W. Hager, H. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search, Publisher, City, 2006.
[15] H.M. Khudhur, Numerical and analytical study of some descent algorithms to solve unconstrained Optimization problems, in: University of Mosul college Computer Sciences and Mathematics Department of Mathematics Iraq, 2015, pp. 83-83.
[16] K.K. Abbo, Y.A. Laylani, H.M. Khudhur, A NEW SPECTRAL CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION, Publisher, City, 2018.
[17] K.K. Abbo, Y.A. Laylani, H.M. Khudhur, Proposed new Scaled conjugate gradient algorithm for Unconstrained Optimization, Publisher, City, 2016.
[18] N. Andrei, An Unconstrained Optimization Test Functions Collection, Publisher, City, 2008.
[19] K.K. Abbo, H.M. Khudhur, New A hybrid Hestenes-Stiefel and Dai-Yuan conjugate gradient algorithms for unconstrained optimization, Publisher, City, 2016.
[20] K.K. Abbo, H.M. Khudhur, New A hybrid conjugate gradient Fletcher-Reeves and Polak-Ribiere algorithm for unconstrained optimization, Publisher, City, 2016.
[21] H.N. Jabbar, K.K. Abbo, H.M. Khudhur, Four--Term Conjugate Gradient (CG) Method Based on Pure Conjugacy Condition for Unconstrained Optimization, Publisher, City, 2018.
[22] E.D. Dolan, J.J. Moré, Benchmarking optimization software with performance profiles, Publisher, City, 2002.