Two classes of spectral conjugate gradient methods for unconstrained optimizations

The spectral conjugate gradient method is effective iteration method for solving large-scale unconstrained optimizations. In this paper, using the strong Wolfe line search to yield the spectral parameter, and giving two approaches to choose the conjugate parameter, then two classes of spectral conjugate gradient methods are established. Under usual assumptions, the proposed methods are proved to possess sufficient descent property and global convergence. Taking some specific existing conjugate parameters to test the validity of the two classes of methods, and choosing the best method from each class to compare with other efficient conjugate gradient methods, respectively. Large-scale numerical results for the experiments are reported, which show that the proposed methods are promising.