Nonlinear Conjugate Gradient Methods For Optimization And Nonlinear System Of Equations.

In this thesis, we study nonlinear conjugate gradient methods for solving uncon-strained optimization problems and nonlinear systems of equation. We investigate theglobal convergence property and numerical performance of these methods.In Chapter 2, based on the three-term modified PRP method proposed by Zhang,Zhou, Li [22] and the two-term modified PRP proposed by Cheng [58], we proposea family of modified descent PRP method. A common property of the method isthat the descent property is independent on the lined search used. Under appropriateconditions, we show that the method is globally convergent. The reported numericalresults show that the method is e?cient.In Chaper 3, based on the two-term modified descent PRP proposed by Cheng[58], we propose a modified HS method for large-scale nonlinear systems of equations.Under appropriate conditions, we show that the method is globally convergent. Thereported numerical results show that the method is e?cient.