A mixed LS-CD spectral conjugate gradient method for uncontrained nonlinear optimization

In order to find a good convergence and numerical expression of unconstrained optimization algorithm at the same time, concentrate on conjugate gradient method and spectral conjugate gradient method with two directions regulatory parameters. This paper presents a conjugate parameter with combining the LS method and the CD method and the corresponding spectral parameter. Based on the parameters, a new spectral conjugate gradient algorithm is proposed which uses the standard Wolfe line search, and the descent property and the global convergence of the algorithm are proved. The given numerical results show that the proposed algorithm is efficient and suitable for solving large-scale unconstrained nonlinear optimization problems. The study result indicates that suitable configuration of two parameters of spectral conjugate gradient method helps reduce the convergence conditions, and enhances the applicability of the algorithm.