Strong and total Fenchel dualities for robust convex optimization problems

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• 作者：Mengdan Wang (1)
  Donghui Fang (1)
  Zhe Chen (2)
  
  1. College of Mathematics and Statistics ; Jishou University ; Jishou ; 416000 ; P.R. China
  2. Business School ; Sichuan University ; Chengdu ; 610064 ; P.R. China
  
• 关键词：90C25 ; 90C46 ; constraint qualification ; strong duality ; total duality ; converse duality ; robust optimization problems
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,262 KB
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• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

In this paper, we present some strong and total Fenchel dualities for convex programming problems with data uncertainty within the framework of robust optimization in locally convex Hausdorff vector spaces. By using the properties of the epigraph of the conjugate functions, we give some new constraint qualifications, which characterizes completely the strong duality and the stable strong duality. Moreover, some sufficient and/or necessary conditions for the total duality and converse duality are also obtained.