一个新的解非线性对称方程组的非单调共轭梯度方法

给出一个新的解非线性对称方程组：g（x）=0（x∈R^n,g：R^n→R^n连续可微,并且其雅克比矩阵g（x）在x∈R^n上对称）的非单调共轭梯度方法,分析新方法的全局收敛性,并用数值实验来检验其有效性.新方法全局收敛,在不执行任意线搜索的条件下能够确保搜索方向的下降性,而且初始点的选择与维数的增加并不明显影响检验结果.

A New Nonmonotone Conjugate Gradient Method for Symmetric Nonlinear Equations

A new nonmonotone conjugate gradient method is presented for solving symmetric nonlinear equations g（x）=0（x∈R^n,g：R^n→Rn is continuously differentiable and its Jacobian g（x）is symmetric for all x∈R^n）.The global convergence of the method is established under suitable conditions.Numerical results show that this method is effective.The search direction is descent without any line search technique.Moreover,the initial points and the increase of dimension don＇t influence the performance of the presented method.