Hattan Zain Al-Abdin Tawfiq2022-05-182022-05-184910https://drepo.sdl.edu.sa/handle/20.500.14154/2906Line search is a major component in the structure of the conjugate gradient method to solve unconstrained optimization problems. But its exact implementation to nonquadratic functions is unlikely in most of the cases. This thesis deals with a self contained study of inexact line search and its effect on the convergence of certain modifications and extensions of the conjugate gradient method. We describe in detail various algorithms due to these extensions and apply them to some of the standard test functions.enThesis