有界约束非线性方程组的不精确牛顿类仿射共轭梯度路径方法

An inexact Newton affine scaling conjugate gradient path method for bound-constrained nonlinear systems

提供了不精确牛顿类的仿射内点离散共轭梯度法求解有界变量约束的非线性方程系统.通过构建仿射离散共轭梯度路径结合不精确牛顿步获得了搜索方向,并使用内点回代线搜索技术获得迭代步长.在合理的条件下,证明了算法的整体收敛性和局部超线性收敛速率.最后,数值结果表明了所提供的算法的有效性和可行性.

We propose an inexact Newton arlene scaling interior discrete conjugate gradient path method for solving nonlinear equality systems subject to bounds on the variable. By constructing an affine scaling discrete conjugate gradient path, we obtain an iterative search direction. By combining the interior backtracking line search, we find an acceptable trial step size. The global convergence and the local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate that the algorithm is effective and feasible.