An efficient hybrid three-term conjugate gradient method with practical applications

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آذر 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.95643.1739

نویسندگان

Youcef Elhamam Hemici^* ؛ Samia Khelladi؛ Djamel Benterki

Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Setif1 University-Ferhat Abbas , 19000, Algeria.

چکیده

The conjugate gradient method is widely used for large-scale unconstrained optimization due to its efficiency in iteration number and computing time. In this paper, we present a new parameter $\beta_{k}$ by hybridizing the Liu-Storey parameter $\beta_{k}^{LS}$ and its modification $\beta_{k}^{DLS}$. We also use a hybrid three-term technique ensuring sufficient descent based on strong Wolfe conditions. We prove that the new direction possesses the descent property and that the corresponding algorithm is globally convergent. Numerical experiments on test problems and some applications, such as image restoration and sparse signal recovery, further show that our approach is efficient, consistently outperforming other approaches in terms of convergence speed and solution quality.

کلیدواژه‌ها

Unconstrained optimization؛ Conjugate gradient method؛ Descent direction؛ Image restoration؛ Signal recovery