Issue |
RAIRO-Oper. Res.
Volume 57, Number 2, March-April 2023
|
|
---|---|---|
Page(s) | 333 - 350 | |
DOI | https://doi.org/10.1051/ro/2023010 | |
Published online | 15 March 2023 |
Two modified conjugate gradient methods for solving unconstrained optimization and application
1
Laboratory Informatics and Mathematics (LIM), Mohamed Cherif Messaadia University, Souk Ahras 41000, Algeria
2
Mohamed Cherif Messaadia University, Souk Ahras 41000, Algeria
* Corresponding author: a.mehamdia@univ-soukahras.dz
Received:
27
July
2022
Accepted:
27
January
2023
Conjugate gradient methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems as they do not require the storage of any matrices. In order to obtain a theoretically effective and numerically efficient method, two modified conjugate gradient methods (called the MCB1 and MCB2 methods) are proposed. In which the coefficient βk in the two proposed methods is inspired by the structure of the conjugate gradient parameters in some existing conjugate gradient methods. Under the strong Wolfe line search, the sufficient descent property and global convergence of the MCB1 method are proved. Moreover, the MCB2 method generates a descent direction independently of any line search and produces good convergence properties when the strong Wolfe line search is employed. Preliminary numerical results show that the MCB1 and MCB2 methods are effective and robust in minimizing some unconstrained optimization problems and each of these modifications outperforms the four famous conjugate gradient methods. Furthermore, the proposed algorithms were extended to solve the problem of mode function.
Mathematics Subject Classification: 90C30 / 65K05 / 62G05
Key words: Unconstrained optimization / conjugate gradient method / numerical comparisons / mode function / kernel estimator
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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