Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (1): 20-30.

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Strong Fenchel-Lagrange Duality for Convex Optimization Problems with Composite Function

Donghui Fang*,Liping Tian(),Xianyun Wang()   

  1. College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000
  • Received:2018-08-30 Online:2020-01-26 Published:2020-04-08
  • Contact: Donghui Fang E-mail:littleequation@163.com;495102048@qq.com
  • Supported by:
    国家自然科学基金(11861033);湖南省教育厅科研基金(17A172)

Abstract:

In this paper, we consider a convex composite optimization problem which consists in minimizing the sum of a convex function and a convex composite function. By using the properties of the epigraph of the conjugate functions, some sufficient and necessary conditions for the strong and stable strong Fenchel-Lagrange dualities are provided.

Key words: Fenchel-Lagrange duality, Constraint qualification, Convex composite optimization problem

CLC Number: 

  • O224
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