A spectral conjugate gradient method under modified nonmonotone line search technique

In this paper,we introduce a spectral Conjugate Gradient direction, which have the properties of both HS conjugate gradient method and PRP conjugate gradient method via introducing parameter λ, Motivated by the ideas of introducing parameter, we give a modified nonmonotone line search by doing convex combination. besides we introduce a new nonmonotone line search, and propose the algorithm of nonmonontone spectral conjugate gradient method, then the convergence of new nonmonotone spectral Conjugate Gradient method is established under mild conditions. in the end, some some numerical experiments are given.