Study On Several Conjugate Gradient Methods

The nonlinear conjugate gradient method, which was used for solving unconstrained optimization problems, is an important component of optimization methods. The Conjugate gradient method can be not only extensively applied to the science, engineering, economy and management system, but also to the governments'decision-making, manufacturing management, transportation and military and national defense.At the first, this paper introduced the referring conception of unconstrained nonlinear optimization method and some main and simple solves of the problem had been supplied , indicate the basic referring definition and introduction about conjugate gradient. and then, the paper conclude and discussed the Dai-Yuan conjugate gradient method,Beale-Powell restart conjugate gradient method and so on. Basic on the former studies, the paper focus on a modified PRP conjugate gradient method and two modified HS gradient methods. At the end ,the paper look forward and discussed the development of conjugate gradient menthod.The main results obtained in this dissertation can be summarized as follows:â‘ The author proposed new PRP conjugate gradient method ,improve its sufficient decent propert and global convergence under the wolf line search . Some preliminary numerical results later reveal that the new algorithm is efficient.â‘¡Basic on the former studies, indicate two new modified gradient methods, improve these methods's global convergence under the wolf line search without decent propert.