Conjugate Gradient Method

Nonlinear conjugate gradient methods are a class of important methods for optimization. The methods are often used to solve large-scale nonlinear optimization problems for their simple algorithms and small storage requirement. Now, the rapid development of computer and occurrence of a great deal of large-scale optimization problems make the researches in conjugate gradient method revive. This paper presents some new conjugate gradient methods for unconstrained optimization. The structure of this paper is organized as follows:In chapter 1, we introduce the origin, research motivation and development of conjugate gradient methods.In chapter 2, we generalize the method proposed in paper [7] by setting a range of the main parameter β_k of conjugate gradient methods. What's more, we combine this method with the technique of nonmonotone line search, provide a new nonmonotone conjugate gradient algorithm, analyze its convergent properties, and test its numerical efficient.In chapter 3, we present a class of conjugate gradient methods with a new conjugacy condition by applying the idea of paper [10]. Its global convergence is proved under suitable conditions. The numerical results show that this method is competitive with PRP method.