Several Kinds Of Spectral Conjugate Gradient Methods

Nonlinear conjugate gradient methods are a class very important optimization methods. They are especially suitable for solving large-scale unconstrained optimization problems, because of its simple iteration, easy coding and low storage requirements.In this paper, inspired by Cheng and Liu, we present several spectral conjugate gradient methods by using modified line search directions, which have the su?cient descent property independent of any line search conditions and conjugate gradient parameters,and prove their global convergence under suitable line search conditions.The main structure of this paper summarized as follows:In chapter 1, nonlinear conjugate gradient methods and the research status are simply reviewed.In chapter 2, based on the improvement of Yao and Zhang, we generalize the NHS,VLS methods to spectral conjugate gradient methods, get two new methods using WY-L shape parameters called the SNHS and SVLS method. Under the condition of the modified strong Wolfe line search conditons proved the convergence of the two methods.Numerical results show the modified methods are e?ective.In chapter 3, on the basis of improvement of Jiang Xianzhen etc, we generalize the JNP, JVP type of methods to the spectral conjugate gradient methods, get a class of conjugate gradient method using Jiang Xianzhen type parameters, and prove their global convergence under strong Wolfe line search conditions. Numerical results show that the modified methods are e?ective.In chapter 4, inspired by Jiang and Jian, we modify the conjugate gradient parameter of PRP, HS and LS method to the forms with interference factor, generalize them to spectral conjugate gradient method, and prove the global convergence under strong Wolfe line search conditions. Numerical results show that they are effective.