A modified of nonmonotone spectral conjugate gradient method for unconstrained optimization

According to a modified parameter βk, a new nonmonotone spectral Conjugate Gradient method for unconstrained optimization is proposed in this paper,which combines the conjugate gradient direction with spectral step-length effectively. We applied the spectral step-length to the entire Conjugate Gradient direction rather than the negative gradient direction,and take advantage of the new nonmonotone F-rule for line searches to obtain the next iteration point. The global convergent propertise of the algorithm with the modified parameter and the proposed nonmonotone F-rule for line search are proved under some appropriate conditions.