解决非线性互补问题非光滑牛顿算法的全局收敛以及局部收敛性分析

The Analysis of Global and Local Convergence of Nonsmooth Newton Methods for Nonlinear Complementarity Problems

考虑基于Facchinei F等(1997)提出的解决非线性互补问题的非光滑牛顿算法的收敛性质.对该算法我们在较弱的条件下给出了一般性的全局收敛结果,改进了Facchinei F(1997)和Dan H(2002)文中的相关结果,作为这个定理的推论,我们得到的迭代序列的每一个聚点x*或者是非线性互补问题的解或者是稳定点.最后,在局部误差界的条件下给出了超线性(二阶)收敛速度的证明.

In this paper, the convergence properties of the nonsmooth newton algorithm for solving nonlinear complementarity problems based on the paper of Facchinei F（1997） are considered. For this algorithm, a more general global convergence result under mild conditions is given, which improves the corresponding results in the papers of Facchinei F （1997） and Dan H （2002）. As a corollary of the global convergence theorem, every accumulation point x ^＊ of the iteration sequence is generated by the nonsmooth newton algorithm is a solution of nonlinear complementarity problem or a stationary point. Finally, the superlinearly quadratically convergent theorem is presented.