Spectral Conjugate Gradient Methods with the Generalized Quasi-Newton Equation

In order to solve the global optimization problem in engineering and management, Spectral conjugate gradient methods are used in this paper. By introducing the generalized quasi-Newton condition, a class of spectral conjugate gradient with different β_k are formulated. According to different parameters alternative, a comparison to different parameters are given. We also proved the convergence of these formulas that have been established. The numerical example show that conjugate gradient methods are efficient methods for unconstrained optimization.