  In this paper, we propose a new non-monotone conjugate gradient method for
solving unconstrained nonlinear optimization problems. We first modify the
non-monotone line search method by introducing a new trigonometric function to
calculate the non-monotone parameter, which plays an essential role in the
algorithm's efficiency. Then, we apply a convex combination of the
Barzilai-Borwein method for calculating the value of step size in each
iteration. Under some suitable assumptions, we prove that the new algorithm has
the global convergence property. The efficiency and effectiveness of the
proposed method are determined in practice by applying the algorithm to some
standard test problems and non-negative matrix factorization problems.
