Further Studies On The DDL And LWQR Conjugate Gradient Methods

The nonlinear conjugate gradient algorithm is an important algorithm for solving large-scale unconstrained optimization problems,because it has the advantages of simple iteration,small amount of computation and small storage space.Conjugate gradient algorithm has also been concerned by many scholars.In recent years,many advances have been made in the study of conjugate gradient methods.This paper is based on the existing research results of nonlinear conjugate gradient algorithm.The main contents and results are as follows:In chapter 1,this paper introduces several common methods for solving unconstrained optimization problems and their advantages and disadvantages,and then introduces several commonly used lines in the proof of the nonlinear conjugate gradient search algorithm,the research status quo of nonlinear conjugate gradient method are reviewed.In chapter 2,the DDL method proposed by Babaie-Kafaki S and Ghanbari R is further studied and modified:the parameters in the DDL method are generalized,and the theory after the generalization is generalized before the generalization.And then the DDL method is truncated to get DDL+,and the modified method does not depend on the line search to be fully degraded and in the standard Wolfe line Under the search condition,the global convergence of the general function is obtained,and the algorithm is compared with some existing algorithms with good numerical performance under the approximate Wolfe line search[38].numerical results show that the new method is effective.In chapter 3,based on the MHS conjugate gradient algorithm proposed by Dai Zhifeng et al.,We modify DDL method and LWQR method proposed by Liu et al.,and propose two modified nonlinear conjugate gradient methods,called MDDL and MLWQR method.The sufficient descent property of new methods does not depend on the line search conditions,global convergence of the MDDL method and MDDL method are proved under the Wolfe line search conditions or the Armijo line search conditions.The results of the modified algorithm and the modified algorithm are compared with the approximate Wolfe line search[38].The results show that the modified new method is effective.