双扰动多目标规划的锥次微分稳定性  

The Cone-Subdifferential Stability of Multiobjective Programming under Two-Perturbations

作　　者：李杉林[1] 胡毓达 

机构地区：[1]太原师范专科学校数学系,太原030001 [2]上海交大应用数学系,上海200030

出　　处：《运筹学学报》1999年第4期65-70,共6页Operations Research Transactions

基　　金：国家自然科学基金

摘　　要：关于多目标规划解的稳定性问题，一些学者在半连续意义下曾得到比较系统的结果．以后，在锥次微分意义下又获得了更深入的描述．近年，则进一步对目标和约束，以及确定目标空间序的控制锥均受扰动的多目标规划研究其解的稳定性问题，并在Ｂａｎａｃｈ空间和半连续的意义下，得到了很好的刻划．本文则对这类双扰动多目标规划问题，在局部凸拓扑向量空间和锥次微分的意义下，获得了相应的稳定性结论。The stability problems of solution sets of multiobjective programming in finitedimensional vector spaces has been studied by several scholars and obtained more systematic rerults.In Banach spaces,sufficient conditions that ensure the semicontinuty of the solution set maps with respect to two-perturbations which are perturbation of feasible solution sets and objective functions and perturbation of cones has been provided.In the present paper) the existence of the cone-subdifferential of the point-set maps with respect to two-perturbations is discussed. Meanwhile.The cone-subdifferential stability of outcome set maps of multiobjective programming with respect to two-perturbations is getted in local convex topological vector spaces.

关 键 词：多目标规划 锥次微分 稳定性 锥有效点 锥有效解 

分 类 号：O221[理学—运筹学与控制论]