线性互补问题的阻尼牛顿法的有限终止性

ON THE FINITE TERMINATION OF THE DAMPED-NEWTON ALGORITHM FOR LINEAR COMPLEMENTARITY PROBLEM

在[2]中，Harker和Pang提出了如下一个公开问题：对于线性互补问题的阻尼牛顿算法，当它收敛时，算法是否能在有限步内终止？本文对此问题给出一个肯定回答，而且进一步给出一个新的求解一般线性互补问题的有限终止算法．这个算法避免了阻尼牛顿算法可能不收敛的情形．

in [2], Harker and Pang proposed the following open question: whether or notthe damped--Newton algorithm for solving the linear complementarity problems is finite if itconverges. This paper gives an affirmative answer to this question. Moreover, a new finitetermination algorithm for solving general linear complementarity problems is developed toavoid the possibility of the non-convergence of the previous damped-Newton method.