New families of hybrid conjugate gradient descent directions for nonlinear optimization with practical applications

Abstract

This thesis focuses on solving unconstrained nonlinear optimization problems using conjugate gradient methods. We propose new families of search directions of the conjugate gradient method, based on new conjugacy parameters. For each variant, we establish the descent condition of the new search directions, and we proved the global convergence of the corresponding algorithms, under the strong Wolfe conditions. The efficiency of the proposed algorithms is confirmed through numerical tests carried out on several large-scale classical test problems as well as several practical applications