求解变分不等式的Newton迭代的半局部收敛性分析

Semilocal Convergence Aanalyses of the Newton Method for the Variational Inequality

分析了求解变分不等式Newton方法的半局部收敛性,建立了类似于Kantorovich定理的收敛性结果。该结果不仅为判断Newton方法的收敛性提供了可计算的充分条件,也给出了Newton方法的收敛域以及问题解的存在区域。同时,文章也得到了Newton方法的若干收敛性质,包含收敛阶以及可计算的误差估计式等。

The paper establishes a Kantorovich\|like semilocal convergence theorem of the Newton method for the variational inequality. The theorem not only provides the computationally verifiable conditions for insuring the convergence of the Newton method, but also provides the convergence domain of the method and the enclosure of the solution to the problem. Several convergence properties, including the convergence order and the computational error estimation, are also derived.