GUS-property for Lorentz cone linear complementarity problems on Hilbert spaces  

作　　者：MIAO XinHe HUANG ZhengHai 

机构地区：[1]Department of Mathematics, Tianjin University, Tianjin 300072, China

出　　处：《Science China Mathematics》2011年第6期1259-1268,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No. 10871144);the Natural Science Foundation of Tianjin Province (Grant No. 07JCYBJC05200)

摘　　要：Given a real(finite-dimensional or infinite-dimensional) Hilbert space H with a Jordan product,we consider the Lorentz cone linear complementarity problem,denoted by LCP(T,Ω,q),where T is a continuous linear operator on H,ΩH is a Lorentz cone,and q ∈ H.We investigate some conditions for which the problem concerned has a unique solution for all q ∈ H(i.e.,T has the GUS-property).Several sufficient conditions and several necessary conditions are given.In particular,we provide two suficient and necessary conditions of T having the GUS-property.Our approach is based on properties of the Jordan product and the technique from functional analysis,which is different from the pioneer works given by Gowda and Sznajder(2007) in the case of finite-dimensional spaces.Given a real（finite-dimensional or infinite-dimensional） Hilbert space H with a Jordan product,we consider the Lorentz cone linear complementarity problem,denoted by LCP（T,Ω,q）,where T is a continuous linear operator on H,ΩH is a Lorentz cone,and q ∈ H.We investigate some conditions for which the problem concerned has a unique solution for all q ∈ H（i.e.,T has the GUS-property）.Several sufficient conditions and several necessary conditions are given.In particular,we provide two suficient and necessary conditions of T having the GUS-property.Our approach is based on properties of the Jordan product and the technique from functional analysis,which is different from the pioneer works given by Gowda and Sznajder（2007） in the case of finite-dimensional spaces.

关 键 词：Lorentz cone linear complementarity problem Jordan product Lorentz cone 

分 类 号：O221[理学—运筹学与控制论] O177.1[理学—数学]