A descent-safeguarded PRP-type conjugate gradient with global convergence and CUTEst benchmarks

Ahmad Alhawarat; Sultanah Masmali; Shahrina Ismail; Hamid El Hor

doi:10.46481/jnsps.2026.3118

Authors

Ahmad Alhawarat
Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan
Sultanah Masmali
Department of Mathematics, College of Science, Jazan University, Jazan, Saudi Arabia
Shahrina Ismail
[email protected]

Financial Mathematics Program, Faculty of Science and Technology, Universiti Sains Islam Malaysia, Bandar Baru Nilai, 71800 Nilai, Negeri Sembilan, Malaysia
Hamid El Hor
Sidel-Simulations, D-63303 Dreieich, Germany

Keywords:

Conjugate gradient method, global convergence, CUTEst benchmarks, unconstrained optimization

Abstract

Conjugate gradient (CG) methods are widely used for solving large-scale unconstrained optimization problems. Well-known methods, such as the Polak-Ribière-Polyak and Hestenes-Stiefel methods, may not satisfy the global convergence property. To improve this behavior, this paper constructs a new three-term CG method based on the PRP framework. The proposed method is shown to satisfy sufficient descent and global convergence properties. To study its behavior, we compare its performance with those of CG-Descent 6.8, the non-negative Dai-Liao method, and the HS+TA method by applying them to more than 180 optimization problems selected from the CUTEst library. The numerical results show that the new method performs better than the three competing methods and other recently published CG methods in terms of the number of iterations, the number of function and gradient evaluations, and the CPU time required to solve the test problems. To illustrate accuracy, we report the function and gradient values at the obtained solutions for all test problems.

Dimensions

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