摘要
在不变凸的假设下来讨论多目标半定规划的最优性条件、对偶理论以及非凸半定规划的最优性条件.首先给出了非凸半定规划的一个KKT条件成立的充分必要条件,并利用此定理证明了其最优性必要条件.其次讨论了多目标半定规划的最优性必要条件、充分条件,并对其建立Wolfe对偶模型,证明了弱对偶定理和强对偶定理.
This paper aims at the optimality conditions, duality of multiobjec- tive semidefinite programming problems and the optimality conditions for nonconvex semidefinite programming. We first obtain a necessary and sufficient conditions of KKT condition for nonconvex semidefinite programming, based on this result, the optimality necessary conditions are presented. Furthermore, we discuss the optimality necessary or sufficient conditions for multiobjective semidefinite programming and construct Wolfe dual model for the corresponding problem. Finally, weak and strong duality theorems are established.
出处
《运筹学学报》
CSCD
北大核心
2016年第3期68-78,共11页
Operations Research Transactions
基金
国家自然科学基金(No.11601050)
重庆市自然科学基金(No.cstc2016jcyjA0116)
重庆市教委基金(No.KJ1600316)
关键词
非凸半定规划
多目标半定规划
KKT条件
不变凸
nonconvex semidefinite programming, multiobjective semidefinite pro-gramming, KKT conditions, invex
