New contributions to nonlinear optimization methods

Abstract

This thesis presents a theoretical and numerical study of various methods for solving nonlinear optimization problems, with a particular focus on conjugate gradient methods. In this context, we propose an enhancement of the Polak–Ribière–Polyak method by introducing a new steplength. Furthermore, two novel approaches have been developed for the unconstrained minimization of nonlinear and differentiable cost functions. The numerical results demonstrate that the proposed methods offer significant improvements in solving large-scale problems, thereby enhancing the overall performance of these algorithms in practical applications.