Abstract

Abstract
This thesis delves into the exciting realm of nonlinear conjugate gradient (CG) methods, a powerful set of algorithms designed to tackle unconstrained optimization problems – particularly those characterized by many variables. These problems are increasingly prevalent in various scientific fields.
We propose a series of CG methods, meticulously crafted to enhance the efficiency and effectiveness of finding the minimum point of the objective function. Additionally, we ensure that each step taken by the algorithm leads to a significant reduction in the function’s value. This is especially crucial when combined with the strong Wolfe line search, a powerful optimization technique that guarantees significant progress towards the minimum.
To validate our proposed methods, we conducted extensive numerical experiments. The results convincingly demonstrate the robustness and efficiency of these new approaches compared to existing CG methods. They offer a faster and more reliable path for minimizing objective functions in unconstrained optimization problems. This thesis doesn’t stop at unconstrained optimization. Recognizing the versatility of our CG methods, we embark on a journey to explore their applicability in a broader domain: nonparametric statistics. We strategically enhance our algorithms to tackle two key challenges in this (mode function estimation and regression function estimation). By successfully applying our CG methods to these problems, we demonstrate their potential to significantly contribute to the field of nonparametric statistics.
Key words: Unconstrained optimization, Strong Wolfe line search, Sufficient descent condition, Global convergence, Numerical comparisons, Mode function, Regression function.

Information

Item Type:	Thesis
Divisions:	» Faculty of Science and Technology
ePrint ID:	4945
Date Deposited:	2024-05-23
Further Information:	Google Scholar
URI:	https://www.univ-soukahras.dz/en/publication/article/4945

BibTex