Study On Global Convergence Of Several Conjugate Gradient Methods With Parameters

The nonlinear conjugate gradient (CG) method, which was used for solving unconstrained optimization problems, is an important component of optimization methods. The CG 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.The global convergence properties of nonlinear conjugate gradient method which contain parameters are studied in this dissertation. To the refered DY method and the FR method, the global convergence property is studies with Wlofe search, which the preliminary numerical results indicate that the proposed methods are very promising. The global convergence property, with the Armijo line search, of refered FR method, PRP method and LS method, is discussed. And the context of this dissertation and concluding with the main results obtained in this dissertation.The main results obtained in this dissertation can be summarized as follows: basic on the introductions of the nonlinear conjugate gradient methods and the global convergence of them:â‘ The author proposed a class of new conjugate gradient method of dependent DY method of containing parameters in chapter 2, which has good properties as the DY method, and the global convergence properties of the new method are proved by the standard Wolfe line search. Some preliminary numerical results reveal that the new algorithm is efficient.â‘¡A new conjugate gradient method of concerning FR method is developed. The author investigates the global convergence of the new method with the generalized Wolfe line search and the predigest Armijo line search which was proposed by Lian et al., and obtains the good experimentation results.â‘¢The author explores the global convergence properties of the PRP method and LS method with the Grippp-Lucidi line search, and gets the efficient numerical results.â‘£A class of conjugate gradient methods, which can be regarded as certain kind of convex combination of the FR method and DY method, were developed by the author. The parameter of the method is generalized, and under appropriate conditions the global convergence of the class of conjugate gradient methods are shown with the two Armijo-type line searches.