关于单调线性矩阵互补问题的势函数约减法

Potential Reduction Method about the Monotone Linear Complementary Problem in Matrices

线性矩阵互补问题是从欧式空间下的线性互补问题推广得到的,最早由M.Kajima等人提出,同时给出了该问题的内点法的理论框架及若干算法。文中构造了一个势函数的约减函数,借用路径跟踪法的思想构造算法,并证明了该算法的可行性及收敛性。

The linear complementary problems in matrices were proposed by M·Kajima at first,which were based on the linear complementary problems in the Euclidean space.At the same time,Kajima designed the interior point-algorithms＇ theory frame for solving monotone linear matrix complementary problems.In this paper,the author designed the potential reduction function to solve monotone linear complementary problems in symmetric matrices,and proved that the algorithm is feasible and convergent.