An Improved Spectral Conjugate Gradient Algorithm for Nonconvex Unconstrained Optimization Problems

In this paper, an improved spectral conjugate gradient algorithm is developed for solving nonconvex unconstrained optimization problems. Different from the existent methods, the spectral and conjugate parameters are chosen such that the obtained search direction is always sufficiently descent as well as being close to the quasi-Newton direction. With these suitable choices, the additional assumption in the method proposed by Andrei on the boundedness of the spectral parameter is removed. Under some mild conditions, global convergence is established. Numerical experiments are employed to demonstrate the efficiency of the algorithm for solving large-scale benchmark test problems, particularly in comparison with the existent state-of-the-art algorithms available in the literature.