A New Preconditioned Conjugate Gradient Algorithm

Conjugate gradient method is one of the efficient algorithms for solving unconstrained optimization problems. And it is very suitable for solving large-scale optimization problems due to the simplicity, less computational cost and storage requirements. In this paper, a new preconditioned conjugate gradient algorithm based on new quasi-Newton equation is presented. We prove sufficient descent property and global convergence for general nonlinear functions of the algorithm. And numerical comparison experiment is implemented.This paper includes four chapters. In Chapter 1, we briefly introduce optimization problem and its application. In Chapter 2, we firstly introduce the background of general conjugate gradient method and some common, classic conjugate gradient methods. Then new quasi-Newton equation and the corresponding quasi-Newton method are described. In Chapter 3, we give a new preconditioned conjugate gradient algorithm based on new quasi-Newton equation of the previous chapter. And the sufficient property and global convergence of the algorithm is also proved. In Chapter 4, the numerical comparison experiment about the given algorithm in Chapter 3 is carried out and relevant conclusions are drawn by analyzing numerical results. The theoretic and numerical results show that the new algorithm in this paper is very promising and efficient.