一类锥约束多目标优化问题的高阶对偶研究  

Higher-order duality in multiobjective programming problems with cone constraints

作　　者：李红梅[1] 高英[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《纯粹数学与应用数学》2015年第1期73-84,共12页Pure and Applied Mathematics

基　　金：国家自然科学基金(11201511);重庆市重点实验室专项项目(CSTC;2011KLORSE03)

摘　　要：在一类锥约束单目标优化问题的一阶对偶模型基础之上,建立了锥约束多目标优化问题的二阶和高阶对偶模型.在广义凸性假设下,给出了弱对偶定理,在Kuhn-Tucker约束品性下,得到了强对偶定理.最后,在弱对偶定理的基础上,利用Fritz-John型必要条件建立了逆对偶定理.In this paper, basing on the first-order dual models for single objective problems with cone constraints, we construct second-order and higher-order dual models for nonlinear multiobjective programming problems with cone constraints. And then we establish weak and strong duality theorems under generalized convexity assumptions. By using Fritz-John type necessary condition, converse duality theorems are established.

关 键 词：锥约束多目标优化 广义凸 对偶定理 

分 类 号：O221.6[理学—运筹学与控制论]