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Stable and Total Fenchel Duality for Composed Convex Optimization Problems

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Abstract

In this paper, we consider the composed convex 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 and the subdifferentials of convex functions, we give some new constraint qualifications which completely characterize the strong Fenchel duality and the total Fenchel duality for composed convex optimiztion problem in real locally convex Hausdorff topological vector spaces.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Jishou University, Jishou, 416000, China

    Dong-hui Fang & Xian-yun Wang

Authors
  1. Dong-hui Fang
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  2. Xian-yun Wang
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Correspondence to Dong-hui Fang.

Additional information

Supported by the National Natural Science Foundation of China (No. 11461027), Hunan Provincial Natural Science Foundation of China (No. 2016JJ2099) and the Scientific Research Fund of Hunan Provincial Education Department (No.17A172).

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Fang, Dh., Wang, Xy. Stable and Total Fenchel Duality for Composed Convex Optimization Problems. Acta Math. Appl. Sin. Engl. Ser. 34, 813–827 (2018). https://doi.org/10.1007/s10255-018-0793-3

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  • DOI: https://doi.org/10.1007/s10255-018-0793-3

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