Improved conjugate gradient methods and application to nonparametric estimation

Abd Elhamid Mehamdia¹ ; Yacine Chaib¹

¹ Laboratory Informatics and Mathematics Mohamed Cherif Messaadia University Souk Ahras, 41000, Algeria

Applicationes Mathematicae, Tome 51 (2024) no. 2, pp. 147-161.

Résumé

The conjugate gradient (CG) method is one of the most important ideas in scientific computing, applied to solving linear systems of equations and nonlinear optimization problems. In this paper, based on a variant of Dai–Yuan (DY) method and Fletcher–Reeves (FR) method, two modified CG methods (named IDY and IFR) are presented and analyzed. The search direction of the presented methods fulfills the sufficient descent condition at each iteration. We establish the global convergence of the proposed algorithms under normal assumptions and strong Wolfe line search. Preliminary elementary numerical experiment results are presented, demonstrating the effectiveness of the methods. Finally, the methods are extended to solve the problem of conditional model regression function.

Détail

DOI : 10.4064/am2512-6-2024

Keywords: conjugate gradient method important ideas scientific computing applied solving linear systems equations nonlinear optimization problems paper based variant dai yuan method fletcher reeves method modified methods named idy ifr presented analyzed search direction presented methods fulfills sufficient descent condition each iteration establish global convergence proposed algorithms under normal assumptions strong wolfe line search preliminary elementary numerical experiment results presented demonstrating effectiveness methods finally methods extended solve problem conditional model regression function