例外簇与线性互补问题的存在性定理

1．简介给定一n×n阶矩阵M和一n维向量q，由M和q决定的线性互补问题是求得一向量x∈Rn使下式成立：问题（1）简记为LCP（q；M）．［1］对此问题作了详细的介绍，其中一个重要专题是研究（1）的解存在性问题：在何种条件下，LCv（q，wr）有解．山给出了各种存在性定理如：当wr是正定矩阵时，对任一qeR”，LCP（q，M）都有唯一解，这一结果被推广到P一矩阵，当M为（严格）半单调矩阵及q（三）＞0时，LCP（q，M）只有零解；当M为协正定阵时，q限制于某一集合时，LCP（q，M）有解等．所有上述结果都源于线性互补问题的二次等价形式及…

EXCEPTIONAL FAMILY AND EXISTENCE THEOREMS IN LINEAR COMPLEMENTARITY PROBLEMS

By introducing the concept of exceptional family discoved by G. Isac, we discussthe relation between the concept and the existence results in linear complementarityproblems. We not only recover many well known results, but also find a new resultrelating to G-matrix class. We also characterize, for the first time, the behavior ofthe multipliers in exceptional families. At last we propose an algorithm generattinga exceptional family, the algorithm has the property that it either finds a solutionof LCP or generates an exceptional family of LCP.