Unconstrained Optimization Of The Spectral Conjugate Gradient Algorithm

By combining the idea of spectral gradient method and conjugate gradient method.We get the spectral conjugate gradient method, which is simple, easily realized, and is especially. It has wide application to many fields, such as, natural science, social science, practical production, engineering design, and modern management, etc. The numerical results show that it can be recognized and effective than PRP method. In view of this, we study the spectral gradient method .It has wide application to many fields, such as, natural science, social science, practical production, engineering design, and modern management,etc.Optimization method is an important part of operations research. It has wide application to many fields, such as, natural science, social science, practical production, engineering design, and modern management,etc. So the research of the optimization algorithm is very important. Nonlinear conjugate gradient method is one of the optimization methods which is simple, easily realized, and is especially suitable for solving the large-scale nonrestraint optimization problems. This paper mainly discusses the spectral conjugate gradient method of the optimization problemIn Chapter 1, nonlinear memory gradient method of the optimization problem is introduced.As the same time the global convergence of the conjugate gradient method is introduced.In chapter 2, the background in the domestic and international are introduced, and the current status of research of the spectrum conjugate gradient method. This article lists the test functions which is required for numerical experimentsIn Chapter 3, Based on Hager-Zhang's conjugate gradient formula .A new spectral conjugate gradient method is proposed in this paper. It proved that the global convergence of corresponding algorithm with the Armijo search was proved. Numerical results shows that the method more efficient and suitable than DY spectrum algorithm, FR spectrum algorithm and PRP spectrum algorithm.In Chapter 4, Based on Hager-Zhang's spectral conjugate gradient method is improved. A new Hager-Zhang's spectral conjugate gradient method is proposed. It proved that the global convergence of corresponding algorithm with the Wolfe search was proved. Numerical results show that this method has good computational efficiency, and stability is better, for solving large scale unconstrained optimization problems.In Chapter 5, A new lterative formula is proposed with the spectral conjugate gradient method. It proved that the global convergence of corresponding algorithm. Numerical experiments show that Wolfe line Search Compared with other algorithms and these two algorithms get better results.