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.

翻译：在本文中,我们提出一种新的非分子同化梯度方法来解决不受限制的非线性优化问题。 我们首先修改非分子线搜索方法, 引入一个新的三角函数来计算非分子参数, 这对于算法的效率至关重要。 然后, 我们应用巴齐赖- 伯文方法的二次组合, 来计算每次迭代的职级大小值。 根据一些适当的假设, 我们证明新的算法具有全球趋同特性。 将算法应用于某些标准测试问题和非负矩阵因子化问题, 从而决定了拟议方法的效率和效力 。