Researches On Theory And Application Of Two Nonlinear Conjugate Methods

Conjugate gradient method has the characteristics of simple iteration and small data storage space,which is widely used in large-scale nonlinear optimization problems in large industry,national defense engineering,chemical engineering and other fields.Therefore,it is of great theoretical significance and practical value to study the conjugate gradient method for solving nonlinear optimization problems efficiently.The research of this paper is mainly divided into the following three parts:In the first part,the mixed conjugate gradient method is created.This method creates a new formula on the basis of the Dai-Yuan(DY)method,combines the new formula with the DY formula,adds the selection of parameters,and recombines into a new mixed conjugate gradient method.This method decreases under the Wolfe inexact line search.The global convergence of the algorithm is given.The results of numerical experiments show that the CZ algorithm is effective.In the second part,a modified FR conjugate gradient method based on the spectral gradient method is established on the basis of the analysis of the classical FR conjugate gradient method.The method combines the conjugate parameters of FR,DY,CD and other six classical FR conjugate gradient methods.In addition,it is proved that the proposed algorithm has a descending direction and global convergence under Wolfe line search.By comparing with the numerical results of the other two algorithms,it is shown that the proposed algorithm has certain advantages.The third part,based on the compressed sensing theory,aims to solve the large-scale sparse signal reconstruction problem.Combined with the two conjugate gradient methods of CZ and CZFR proposed in this paper,the effectiveness of sparse signal reconstruction problem is analyzed and studied by selecting different smooth approximation functions.The comparison with the recovery performance of classical methods shows that the CZ algorithm and CZFR reconstruction have high signal-to-noise ratio and less time consuming,which can be effectively applied to sparse signal recovery.