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多目标半定规划的最优性条件及对偶理论

李永玲1  杨洋1   罗洪林1,*   

  1. 1. 重庆师范大学数学科学学院, 重庆 401331
  • 收稿日期:2015-09-15 出版日期:2016-09-15 发布日期:2016-09-15
  • 通讯作者: 罗洪林 1071025013@fudan.edu.cn
  • 基金资助:

    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)

The optimality conditions and duality theory for multiobjective semidefinite programming

LI Yongling1  YANG Yang1  LUO Honglin1,*   

  1. 1. School of Mathematical Sciences, Chongqing  Normal University, Chongqing 401331, China
  • Received:2015-09-15 Online:2016-09-15 Published:2016-09-15

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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．

关键词: 非凸半定规划, 多目标半定规划, KKT 条件, 不变凸

Abstract:

This paper aims at the optimality conditions, duality of multiobjective 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．

Key words: nonconvex semidefinite programming, multiobjective semidefinite programming, KKT conditions, invex