An efficient hybrid conjugate gradient method for unconstrained optimization and image restoration problems

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 27 شهریور 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.88087.1449

نویسندگان

Choubeila Souli¹؛ Raouf Ziadi^{* 1}؛ Imad Eddine Lakhdari²؛ Assma Leulmi¹

¹Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, Algeria.

²Laboratory of Mathematical Analysis, Probability and Optimizations, Biskra University, Algeria.

چکیده

The conjugate gradient (CG) method is an optimization technique known for its rapid convergence; it has blossomed into significant developments and applications. Numerous variations of CG methods have emerged to enhance computational efficiency and address real-world challenges. In this work, a novel conjugate gradient method is introduced to solve nonlinear unconstrained optimization problems. Based on the combination of PRP (Polak-Ribière-Polyak), HRM (Hamoda-Rivaie-Mamat) and NMFR (New modified Fletcher-Reeves) algorithms, our method produces a descent direction without depending on any line search. Moreover, it enjoys global convergence under mild assumptions and is applied successfully on various standard test problems as well as image processing. The numerical results indicate that the proposed method outperforms several existing methods in terms of efficiency.

کلیدواژه‌ها

Unconstrained optimization؛ Hybrid conjugate gradient؛ Global convergence؛ Image restoration