Nonlinear Conjugate Gradient Algorithm And Its Application

Conjugate gradient method is one of the main methods for solving large-scale unconstrained optimization problems. The conjugate gradient method has many advantages, such as easy operation, small storage requirement and etc. So the conjugate gradient method has important applications for solving large scale optimization problems in the fields of national defense, chemical, aerospace and atmospheric simulation.In the first chapter, based on the newk?, a new nonlinear conjugate gradient method for solving unconstrained optimization problems is considered. Under the appropriate assumptions, the global convergence of the method is given under the Wolfe line search and the generalized Wolfe line search. And the numerical experiments are presented to show the effectiveness of this method.In the second chapter, we use the conjugate gradient method to solve the nonlinear complementarity problems by using the Fischer-Burmeister function to transform the nonlinear complementarity problems into a system of nonsmooth equations. By analysing the properties of merit function, we give different conjugate gradient methods to solve the nonlinear complementarity problems under different Armijo type line searches. And the corresponding global convergence results and the numerical experiments are also given.In the third chapter, we consider the method of solving the nonlinear nonsmooth complementarity problems. Under the condition that the function F is not required to be a continuous differentiable00 RP ? function, a smoothing conjugate gradient method is given by using the smoothing function. We give the global convergence analysis and the related numerical experiments of the method.