A Class of Descent Nonlinear Conjugate Gradient Methods

Abstract

This thesis further study descent conjugate gradient methods based on the modified FR method and the modified PRP method give the class of conjugate gradient methods formed by the convex combination of the MFR method and the MPRP method. This class of methods enjoys the same nice properties as those of the MFR method and the MPRP method. Firstly the methods generate sufficient descent directions for the objective function. This property is independent of the line search used. Secondly if exact line search is used, the methods possess quadratic termination property. Thirdly if Armijo type line search is used, then the methods are globally convergent when used to minimize a general nonconvex function. Finally, we do extensive numerical experiments to test the performance of the members in the class with different parameters. And then compare the performance of one of the method in the class with the MFR method and the MPRP method.