Set-Valued and Variational Analysis

, Volume 24, Issue 2, pp 253–275 | Cite as

Complete Duality for Quasiconvex and Convex Set-Valued Functions

  • Samuel Drapeau
  • Andreas H. Hamel
  • Michael Kupper


This paper provides a unique dual representation of set-valued lower semi-continuous quasiconvex and convex functions. The results are based on a duality result for increasing set-valued functions.


Set-valued functions Quasiconvexity Dual representation Increasing functions Fenchel-Moreau 

Mathematics Subject Classification (2010)

49N15 46A20 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Samuel Drapeau
    • 1
  • Andreas H. Hamel
    • 2
  • Michael Kupper
    • 3
  1. 1.SAIF/CAFR and Mathematics DepartmentShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  2. 2.Free University of BolzanoBrunicoItaly
  3. 3.Konstanz UniversityKonstanzGermany

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