Nonlinear Conjugate Gradient Methods For Unconstrained And Bound-constrained Optimization

In this thesis, we study nonlinear conjugate gradient methods for solving un- constrained and bound-constrained optimization problems, we also discuss the global convergence property and numerical performance of these methods.In Chapter 2, we propose a modified nonlinear LS conjugate gradient method for unconstrained optimization. Under appropriate conditions, we consider the use of a nonmonotone line search technique in the proposed method, and we prove the global convergence of the modified nonlinear conjugate gradient method.In Chapter 3, we propose a nonlinear conjugate gradient method for solving bound-constrained optimization problems, and establish its global convergence theorem. We also do some numerical experiments to show that the proposed method is effective.