线性互补问题的一类新的带参数价值函数的阻尼牛顿法

A New Parameterized Merit Function for Linear Complementarity Problems and a Damped Newton Method

本文给出了线性互补问题LCP(q ,M)的一类新的带参数光滑价值函数 ,基此价值函数提出了一种阻尼牛顿类算法 ,并证明了当M为P 矩阵时 ,该算法全局收敛且有限步终止 .通过数值实验说明了该算法高效可靠 .与互补问题的磨光方程组中所采用的带参数价值函数不同 ,这里的参数最终并不趋向于零 ,而是趋向于被称作解的乘子向量 (与凸非线性极小极大问题的Lagrange乘子完全一致 ) ,这一思想是本文作者首次提出来的 ,同时本文中所采用的阻尼牛顿类方法也有其独到之处 。

A new parameterized smooth merit function for linear complementarity problems  LCP (q,M) was given and a related damped Newton type algorithm was established.Global convergence and finite termination property is obtained when M is a P matrix.Numerical results suggest that the method is efficient and promising.The parameters used in the paper were tend to multipliers (which are identical with the Lagrangian multipliers in the convex nonlinear min max problems) at the solution of  LCP (q,M) instead of zeros which were usually appeared in the smoothing methods for complementarity problems.This idea was first proposed by the authors and the related damped Newton method was new one which would be a powerful method in the field.