向量优化问题强有效点的锥刻画  

On Cone Characterizations of Strong Efficiency in Vector Optimization Problems

作　　者：谭双 TAN Shuang(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《湖北民族学院学报（自然科学版）》2018年第2期147-149,共3页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：国家自然科学基金面上项目(11171363);基础科学与前沿技术研究(重点)(cstc2015jcyj BX0029)

摘　　要：利用集合在某点的相依切锥、法向锥和可行方向锥研究了一般向量优化问题中的全局Pareto真有效点、局部Pareto有效点和强有效点,得到了关于全局Pareto真有效点、局部Pareto有效点锥刻画的两个新的结果,使已有的结果更加完善.同时在非凸的假设条件下给出了强有效点的必要条件,在凸性假设条件下给出了强有效点的充分必要条件.In this paper,global properly Pareto efficient point,local Pareto efficient point and the strong efficient point in vector optimization problems are characterized with the help of contingent,normal cones as well as cones of feasible directions of a set of dependency at some point. We derive two new results about global properly Pareto efficient point,local Pareto efficient point with the help of cones.The existing results are perfected.At the same time,the necessary conditions for the strong effective point are given under the condition of non-convex hypothesis,and the sufficient and necessary condition of the strong effective point is given under the convex hypothesis.

关 键 词：向量优化 真有效点 有效点 强有效点 

分 类 号：O221[理学—运筹学与控制论]