Journal of Global Optimization

, Volume 55, Issue 3, pp 521–538 | Cite as

Abstract convexity of radiant functions with applications



In this paper, we investigate abstract convexity of non-positive increasing and radiant (IR) functions over a topological vector space. We characterize the essential results of abstract convexity such as support set, subdifferential and polarity of these functions. We also give some characterizations of a certain kind of polarity and separation property for non-convex radiant and co-radiant sets.


Monotonic analysis IR function Radiant set Co-radiant set Abstract convexity 

Mathematics Subject Classification

26B25 26A48 


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Copyright information

© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.Department of MathematicsShahid Bahonar University of KermanKermanIran
  2. 2.Department of MathematicsKerman Graduate University of TechnologyKermanIran

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