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Abstract convexity of radiant functions with applications

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  • H. Mohebi

Abstract

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. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • H. Mohebi, 2013. "Abstract convexity of radiant functions with applications," Journal of Global Optimization, Springer, vol. 55(3), pages 521-538, March.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:3:p:521-538
    DOI: 10.1007/s10898-012-9888-1
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    References listed on IDEAS

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    1. Alberto Zaffaroni, 2004. "Is every radiant function the sum of quasiconvex functions?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 221-233, June.
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    Cited by:

    1. Chaoli Yao & Shengjie Li, 2018. "Vector Topical Function, Abstract Convexity and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 717-742, June.
    2. Mohammad Hossein Daryaei & Hossein Mohebi, 2024. "Dual optimality conditions for the difference of extended real valued increasing co-radiant functions," Journal of Global Optimization, Springer, vol. 90(2), pages 355-371, October.
    3. Ying Gao & Xin-Min Yang, 2019. "Properties of the nonlinear scalar functional and its applications to vector optimization problems," Journal of Global Optimization, Springer, vol. 73(4), pages 869-889, April.

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