崔娜^*

（  南京航空航天大学理学院；  ）

摘要： 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，最早是由M.Kajima等人在中提出的，他们同时给出了对于该问题的内点法的理论框架及若干算法。本文构造了一个势函数约减函数，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。
关键词： 单调线性矩阵互补问题; 中心路径; 势函数约减法

cuina^*

（  College of Science, Nanjing University of Aeronautics and Astronautics；  ）

Abstract： 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, we design the potential reduction function to solve monotone linear complementary problems in symmetric matrices, and prove that the algorithm is feasible and convergent.

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