Global convergence of new conjugate gradient methods with application in conditional model regression function

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 اردیبهشت 1403

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.85389.1344

نویسندگان

Yacine Chaib^{1، 2}؛ Mehamdia Abd elhamid^{* 1، 2}

¹Laboratory Informatics and Mathematics (LIM), Souk Ahras, Algeria

²Mohamed Cherif Messaadia University Souk Ahras, Algeria

چکیده

The conjugate gradient method is one of the most important ideas in scientific computing, it is applied to solving linear systems of equations and nonlinear optimization problems. In this paper, based on a variant of the Hestenes-Stiefel (HS) method and the Polak-Ribiere-Polyak (PRP) method, two modified CG methods ( named ` MHS∗ and MPRP∗ ) 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 promise and the effectiveness of the proposed methods. Finally, the proposed methods were further extended to solve the problem of the conditional model regression function.

کلیدواژه‌ها

Conjugate gradient method؛ Inexact line search؛ Descent condition؛ Global convergence؛ Conditional model regression