A New Spectral Three-Term Conjugate Gradient Method for Unconstrained Optimization and Its Application

In this paper, we derive a new conjugate gradient (CG) direction with random parameters which are obtained by minimizing the deviation between search direction matrix and self-scaled memoryless Broyden-Fletcher-Goldfard-Shanno (BFGS) update.We propose a new spectral three-term CG algorithm and establish the global convergence of new method for uniformly convex functions and general nonlinear functions, respectively.Numerical experiments show that our method has nice numerical performance on nonconvex functions and supply chain problems.