Hybird Nonlinear Conjugate Gradient Method And Its Global Convergence

Nonlinear conjugate gradient method is a basic iteration method which is to solvesome large-scale nonlinear unconstrained optimization problem. It has the features of thesimple algorithm and small storage space. In the classical nonlinear conjugate gradientmethod, the convergence and numerical expression of different methods are not identical.In recent years, all kinds of hybrid conjugate gradient methods were widely researched,Seeking the conjugate gradient method with the good convergence and numericalexpression becomes a key point in this subject. This paper mainly studies the hybirdnonlinear conjugate gradient method, puts forward some new algorithms and discusses itsconvergence.Firstly, this paper reviews the emergence, development and characteristics of thenonlinear conjugate gradient method and introduces the classical nonlinear conjugategradient method and the background.Secondly, this paper based on the modified HS method which improves theefficiency of the algorithm and PC method which guarantees the global convergence ofthe algorithm presents a hybrid HS-PC conjugate gradient method. The new algorithmneed not give drop conditions, and the corresponding algorithm in Wolfe line search is theglobal convergence. The numerical experiment shows that the algorithm is effective.Thirdly, a algorithm depends on the step length factor and the search direction,combined with conjugate properties of the conjugate gradient method and assuranceobjective function fully down conditions, this paper designs a new line search, connectwith the parameter, and puts forward a hybrid conjugate gradient method. We present thealgorithm is the global convergent.Finally, CD method using strong Wolfe line search can ensure that each searchdirection is decreased, but the global convergence property is bad. Combining with the CDmethod and LS method, this paper puts forward a new nonlinear conjugate gradientmethod. The new method not only has the descending property, but also has globalconvergence in the promotion Wolfe line search. Finally, the numerical experiment verifise.