Based On Armijo Search Spectral Conjugate Gradient Method Research

Spectrum conjugate gradient method is down gradient method and theconjugate gradient method on the basis of development, it has the advantages ofless storage, less amount of calculation. In recent years, with the rapiddevelopment of technology and the need of engineering personnel to solvepractical problems, as an important method to solve the problem of large scaleoptimization, conjugate gradient method has become a focus in the study ofengineering personnel. While a large number of numerical results show that thespectral conjugate gradient algorithm is more effective than traditional conjugategradient algorithm. Therefore, spectroscopy study of the theory of the conjugategradient method is of great significance.Spectrum conjugate gradient method is proposed in this paper a newformat.δ_kis spectrum coefficient,d kis search direction,α_kis step length factor.On this basis, respectively in three forms, get the corresponding threespectral conjugate gradient method, and prove the convergence of the algorithmunder Armijo search, and through the corresponding numerical experiments withpast spectrum conjugate gradient method is analyzed and compared.The third chapter giveβ_k=β_k^SBA, and proved that the new spectrum underArmijo line search NA fully decline of conjugate gradient method, the globalconvergence. The numerical experiment results show that the method is superiorto SFRA, SPRPA algorithm.The fourth chapter giveβ_k=β_k^SHZ, and proved that the new spectrum underArmijo search Hager-Zhang fully decline of conjugate gradient method, theglobal convergence. Numerical experimental results show that the method hasthe very good computation efficiency.Chapter5giveβ_k=β_k^SLS, and under Armijo search proves that the new LS spectrum fully decline of conjugate gradient method, the global convergence.Numerical experiments show that this algorithm has the very good computationefficiency.