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Is every radiant function the sum of quasiconvex functions?

Author

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  • Alberto Zaffaroni

Abstract

An open question in the study of quasiconvex function is the characterization of the class of functions which are sum of quasiconvex functions. In this paper we restrict our attention to quasiconvex radiant functions, i.e. those whose level sets are radiant as well as convex and deal with the claim that a function can be expressed as the sum of quasiconvex radiant functions if and only if it is radiant. Our study is carried out in the framework of Abstract Convex Analysis: the main tool is the description of a supremal generator of the set of radiant functions, i.e. a class of elementary functions whose sup-envelope gives radiant functions, and of the relation between the elementary generators of radiant functions and those of quasiconvex radiant functions. An important intermediate result is a nonlinear separation theorem in which a superlinear function is used to separate a point from a closed radiant set. Copyright Springer-Verlag 2004

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:2:p:221-233
    DOI: 10.1007/s001860300325
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    Citations

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    Cited by:

    1. Ya-ping Fang & Nan-jing Huang, 2007. "Increasing-along-rays property, vector optimization and well-posedness," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 99-114, February.
    2. A. R. Doagooei, 2015. "Minimum Type Functions, Plus-Cogauges, and Applications," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 551-564, February.
    3. H. Mohebi, 2013. "Abstract convexity of radiant functions with applications," Journal of Global Optimization, Springer, vol. 55(3), pages 521-538, March.
    4. Jean-Paul Penot, 2010. "Are dualities appropriate for duality theories in optimization?," Journal of Global Optimization, Springer, vol. 47(3), pages 503-525, July.
    5. A. Sheykhi & A. R. Doagooei, 2017. "Radiant Separation Theorems and Minimum-Type Subdifferentials of Calm Functions," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 693-711, September.
    6. Erio Castagnoli & Giacomo Cattelan & Fabio Maccheroni & Claudio Tebaldi & Ruodu Wang, 2021. "Star-shaped Risk Measures," Papers 2103.15790, arXiv.org, revised Apr 2022.

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