A NEW CLASS OF CONJUGATE GRADIENT METHOD BASED ON SECANT CONDITION FOR UNCONSTRAINED OPTIMIZATION WITH APPLICATION

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, College of computer science and Mathematics, University of Mosul, Mosul, Iraq.

2 Department of Renewable Energy Techniques Engineering, College of Oil and Gas Techniques Engineering, Northern Technical University, Iraq.

3 Community Medicine, College of Medicine, University of Mosul, Iraq.

4 Abu Sahyoun, Mathematics Lecturer, General Education, Liwa University.

5 General Education Department, College of Computer Sciences and Mathematics, University of Liwa, Abu Dhabi 41002, United Arab Emirates.

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 08 June 2026

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History

  • Receive Date: 29 April 2026
  • Revise Date: 29 May 2026
  • Accept Date: 06 June 2026

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