Several Kinds Of New Nonlinear Conjugate Gradient Method

In the nonlinear optimization, conjugate gradient method is one of the important approaches. This method only needs to get the search direction generated by one iteration and the current point gradient can be operational, can overcome the shortcomings of the steepest descent method of slow convergence speed and can avoid the computation and storage of the matrix of Newton’s method, super linear convergence rate, the algorithm is simple, easy to programming and requires no matrix storage other significant features. Thus in solving large scale optimization problems, such as aerospace, oil exploration, atmospheric simulation and other fields, the conjugate gradient method has been widely applied. Based on the previous research, the conjugate gradient method for the unconstrained optimization problems are analyzed and discussed, the main work is as follows:(1)The first chapter, we introduced the present situation of the conjugate gradient method to produce, research value and research.(2)The second chapter based on the conjugate gradient method with Hiroshi Yabe and Masahiro Takano proposed, based on the parameter μk-1 correction, thus a new conjugate gradient method, expanding the scope of the βk it proves that the new algorithm in the strong Wolfe line search is globally convergent. Finally, through the numerical simulation shows that the method has good numerical performance.(3)The third chapter according to the new value βk given by Chen Jihong, combined with Tian Yajuan put forward line search method, this paper presents a new hybrid algorithm, and the sufficient descent property and convergence is proved.(4)In the fourth chapter, we introduce the research results of FR and CD, and propose a new conjugate gradient method with the advantages of FR and CD. Then the basic properties and the global convergence of the new method in the generalized Wolfe line search is proved.