Several New Mixed Conjugate Gradient Methods

The theory and method of unconstrained optimization problem can be seen everywhere in life.In recent years,methods for solving large-scale unconstrained optimization problems have emerged in an endless stream.Based on the conjugate gradient method as the clue,this paper modified the conjugate coefficient and spectral coefficient formulas on the basis of the existing literature,and put forward three new methods,namely the spectral conjugate gradient method,the modified DY conjugate gradient method and a kind of three-term mixed conjugate gradient method.The specific arrangement is as follows:Firstly,this paper extends the research ideas of Jing Shujie et al.,revises the conjugate gradient algorithm based on PRP formula,and puts forward new conjugate coefficient and spectral coefficient formulas.The global convergence of the proposed algorithm is proved under two kinds of line searches,and the corresponding numerical experiments show that the conjugate gradient method is more effective and can solve most of the test problems.Secondly,a modified DY conjugate gradient method is proposed based on the classical DY formula and the ideas of the original literature.In the precise line search,the two parameters in this paper are equivalent to the DY formula.Through numerical experiments of several test functions,and compared with the methods in literature[59],it is concluded that the CDY1 and CDY2 methods in this paper are more effective.Finally,inspired by JHJ method and N method,a modified three-term mixed conjugate gradient method,namely HCF method,is proposed in this paper.Under certain conditions,HCF method is one of the cases of FR,DY,WYL,MHS,MHS and YWH methods,which are discussed in detail in this paper.Similar to the analysis in the previous two chapters,HCF method in this paper is more effective and has good numerical performance compared with JHJ method and N method.Summarize the work of the full text,and put forward the work that can be carried out in the next step.