Study On Global Convergence Analysis Of Some Nonlinear Conjugate Gradient Methods

Optimization is a subject, which is widely used and rapidly developmental. It studies the optimal solutions of some mathematical definition of problems, that is, to give the practical problems, such as oil exploration, atmospheric modeling, the field of aerospace, and other special large-scale problems, the programme comes from a number of elected optimal programmes.Conjugate direction method is a commonly used and effective method in optimization, which is between the steepest descent method and Newton method. Conjugate direction method only needs to use the information of the first derivative, but it overcomes the shortcoming of the steepest descent method in the slow convergence and avoids the defects of Newton method in storaging and computing the second derivative. Conjugate direction method comes from the study of the minimization problem of the quadratic function, but it can be extended to deal with the minimization problem of non-quadratic function. In this paper, we will study conjugate gradient method, which is the most typical conjugate direction method and has important practical value in the natural sciences, social sciences, actual production, engineering design and management modernization.This paper mainly studies several nonlinear conjugate gradient (NCG) algorithms. The major results obtained in dissertation may be summarized as follows:â‘ Two kinds of NCG methods are given on the basis of PRP and LS method, which can guarantee the sufficient descent property without any line searches. Under Wolfe line searches, the global convergences of the given methods are proved.â‘¡We present a hybrid NCG method which takes the advantages of CD and DY method, and we also prove its descent property and global convergence with Wolfe line searches.â‘¢A new NCG method is proposed on the basis of HS method. Under strong Wolfe line searches, the sufficient descent property and the global convergence of this method is proved.â‘£The global convergences of PLS method is proved under the given kind of new non-linear searches.