A New Type Of Conjugate Gradient Methods

We mainly research a new type of hybrid conjugate gradient methods to unconstrainedoptimization, which not only can guarantee d_k being the sufficient descent direction, butalso perform well from the point of numeical view. The thesis is organized as follows:In Chapter 1, we review the development of the conjugate gradient methods andbriefly introduce two typical types of them.In Chapter 2, we propose a new parameter formulaβ_k^D and study its property. Thenwe propose a new type of hybrid conjugate gradient methods based onβ_k^D, and prove theirglobal convergence property under some mild conditions.In Chapter 3, we aim at modifying the hybrid conjugate gradient methods proposedin Chapter 2. Wei et.al(2004) proposed a class of new quasi-Newton equation B_ks_k-1=y_k^*=y_k-1+A_ks_k-1, where A_k is some matrix. Based on the expression of y_k^*, wegive two modified hybrid conjugate gradient methods. The modified methods are globallyconvergent under some mild conditions.In Chapter 4, We report the numerical results, and explain the advantages of newmethod from numerical view.