Research On Several Types Of Nonlinear Conjugate Gradient Methods With Parameters

Conjugate gradient method(CG method)is a kind of a optimilzation algorithm between the steepest descent method and Newton method.The nonlinear CG method is one of the important method in nonlinear optimization with more than 60 years history.In this paper,we introduce the knowledge-based theory and research status of CG method in the first chapter,the basic assumption would be mentioned as well.and propose our new methods with convergence analysis.Besides,the following chapters revolve around the new methods we proposed,and the effectiveness of new methods would be shown by the numerical results.In chapter 2,we consider a spectral CD conjugate gradient method without any line search is convergent.In chapter 3 and 4,we present the FR-type and DY-type CG method containing three parameters respectively,they satisfies the sufficient descent condition under inexact line search.The analysis of their global convergence are provided,and their numerical experiments are dominant in the comparison between classical CG methods.In chapter 5,we suggest a new CG method with quasi-Newton form.The robustness of this method can be proved by the discussion of the condition number of update matrix.Besides,the presented algorithm is global convergent under the strong Wolfe line search,and the numerical results show its efficiency.