Journal of Global Optimization

, Volume 57, Issue 4, pp 1349–1358 | Cite as

Optimization of the difference of topical functions

  • A. R. Doagooei
  • H. MohebiEmail author


In this paper, we first obtain some properties of topical (increasing and plus-homogeneous) functions in the framework of abstract convexity. Next, we use the Toland–Singer formula to characterize the dual problem for the difference of two topical functions. Finally, we present necessary and sufficient conditions for the global minimum of the difference of two strictly topical functions.


Global optimization Monotonic analysis Abstract convexity Topical function Toland–Singer formula Support set Subdifferential set 

Mathematics Subject Classification (2000)

90C46 26A48 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Mahani Mathematical Research Center and Department of MathematicsShahid Bahonar University of KermanKermanIran
  2. 2.International Center for Science, High Technology & Environmental Sciences, Department of MathematicsShahid Bahonar University of KermanKermanIran
  3. 3.Kerman Graduate University of TechnologyKermanIran

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