Backward Step Control for Global Newton-Type Methods
Backward Step Control for Global Newton-Type Methods
复制标题
全局牛顿型方法的后向步进控制
DOI：
--
复制
发表时间：
2016
影响因子：
2.9
通讯作者：
A. Potschka
中科院分区：
文献类型：
--
作者：
A. Potschka
我们提出并分析了一种新的阻尼方法称为向后一步控制的牛顿型方法的数值解的非线性寻根问题的收敛性的全球化。我们提供并讨论了合理的假设，这意味着收敛的向后一步控制的基础上，广义牛顿路径结合向后分析参数。特别是，收敛到一个特定的解决方案和先验估计的残差减少可以显示。此外，我们可以保证过渡到完整的步骤附近的解决方案，这意味着快速的局部收敛。我们提出了两种算法实现的向后一步控制和应用该方法的一百多个例子，包括比较不同的全球化方法的Rosenbrock函数的最小化，并从CUTEst基准库使用向后一步控制的不精确牛顿法的基础上MINRES的大规模无约束优化问题。
We present and analyze a new damping approach called backward step control for the globalization of the convergence of Newton-type methods for the numerical solution of nonlinear root-finding problems. We provide and discuss reasonable assumptions that imply convergence of backward step control on the basis of generalized Newton paths in conjunction with a backward analysis argument. In particular, convergence to a specific solution and a priori estimates on the residual reduction can be shown. Furthermore, we can guarantee a transition to full steps in the vicinity of a solution, which implies fast local convergence. We present two algorithmic realizations of backward step control and apply the method to more than one hundred examples, including comparisons with different globalization approaches for the minimization of the Rosenbrock function, and to large-scale unconstrained optimization problems from the CUTEst benchmark library using backward step control for an inexact Newton method based on MINRES.