一类非单调对称锥线性互补问题解集的性质

Properties of the solution set of a class non-monotone symmetric Cone linear complementarity problems

本文考虑具有笛卡尔P*(κ)线性映射的对称锥线性互补问题.在一定的条件下,讨论这类问题解集的非空性、紧性、以及凸性.所得结论为设计求解这类问题的算法提供了重要的理论基础.欧几里德若当代数理论是该文分析的主要工具.

In this paper,we consider the symmetric cone linear complementarity problem with a Cartesian P＊（κ） mapping.Under some conditions,we investigate the nonemptyness,the compactness,and the convexity of the solution set of the problem concerned.The results obtained in this paper provide an important theretical basis for designing numerical methods to solve this class of problems.The theory of Euclidean Jordan algebras is a main tool in our analysis.