一类非单调二阶锥互补问题解集的非空性与有界性  

Nonemptyness and Boundedness of the Solution Set for Second-Order Cone Complementarity Problems

作　　者：王勇[1] 黄正海[1] 

机构地区：[1]天津大学理学院数学系,天津300072

出　　处：《应用数学学报》2009年第6期961-968,共8页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10871144);天津市自然科学基金(07JCYBJC05200)资助项目

摘　　要：本文在二阶锥上引入一类新的映射,称之为笛卡尔P_*(κ)映射,它是单调映射的推广.文中讨论涉及这类映射的二阶锥互补问题的解的存在性和解集的有界性.主要结论为:如果所考虑的互补问题是严格可行的,那么它的解集是非空有界的.In this paper, a new class of mappings on the second-order cone, called the Cartesian R＊（κ） mapping, is introduced, which is a generalization of the monotone mapping. The nonemptyness and boundedness of the solution set for the second-order cone complementarity problem with a Cartesian R＊（κ） mapping are investigated. The main result obtained in this paper is that the solution set of the concerned problem is nonempty and bounded if it has a strictly feasible point.

关 键 词：二阶锥互补问题 笛卡尔R＊(κ)映射 解的存在性 解集的有界性 

分 类 号：O221.2[理学—运筹学与控制论]