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A NEW CLASS OF CONJUGATE GRADIENT METHOD BASED ON SECANT CONDITION FOR UNCONSTRAINED OPTIMIZATION WITH APPLICATION | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 خرداد 1405 اصل مقاله (1.82 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.72172.3637 | ||
| نویسندگان | ||
| Basim Abbas Hassan* 1؛ Yeldez J. Subhi2؛ Layla Hadi Jwear3؛ Ismat Suleiman Salem4؛ Ali Joma Alissa5 | ||
| 1Department of Mathematics, College of computer science and Mathematics, University of Mosul, Mosul, Iraq. | ||
| 2Department of Renewable Energy Techniques Engineering, College of Oil and Gas Techniques Engineering, Northern Technical University, Iraq. | ||
| 3Community Medicine, College of Medicine, University of Mosul, Iraq. | ||
| 4Abu Sahyoun, Mathematics Lecturer, General Education, Liwa University. | ||
| 5General Education Department, College of Computer Sciences and Mathematics, University of Liwa, Abu Dhabi 41002, United Arab Emirates. | ||
| چکیده | ||
| The Conjugate gradient algorithms are among the efficient and widely considered numerical algorithms for solving large-scale minimization problems. This is due to their low memory requirement and global convergence properties. This paper constructs a new class of conjugate gradient method based on the famous secant condition and Perry's conjugacy condition for unconstrained optimization and image restoration problems. This study is motivated by recent quasi-Newton methods available in literature. The method's main goal is to use information from the secant condition to dynamically modify the conjugacy direction. It is anticipated that this flexibility will raise the optimization process's general efficiency. The suggested algorithm's convergence qualities are established through theoretical analyzes, guaranteeing its dependability and efficiency. An interesting feature of the proposed method is that the search direction possesses the descent property irrespective of the line search strategies. The global convergence of the proposed algorithm is established for uniformly convex function under the weak Wolfe line search. Furthermore, the paper explores practical applications of the proposed CG algorithm in diverse domains such as image restoration and large-scale optimization models. The efficiency of the proposed method is demonstrated through computational test, comparing the performance with other classical state-of-the-art conjugate gradient algorithms. The results demonstrate the algorithm's efficiency and superior convergence behavior, especially in cases with large-scale and complex optimization landscapes. In summary, this work presents a novel viewpoint on conjugate gradient method and provides a viable path forward for optimization strategies. Practical applications illustrate the versatility of the proposed approach and show its potential impact on effectively tackling real-world optimization difficulties. | ||
| کلیدواژهها | ||
| Conjugate gradient formula؛ Global convergence properties؛ Image restoration؛ Secant condition؛ Unconstrained optimization | ||
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آمار تعداد مشاهده مقاله: 2 |
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