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Minimum Type Functions, Plus-Cogauges, and Applications

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  • A. R. Doagooei

    (Shahid Bahonar University of Kerman)

Abstract

In this paper, the concept of plus-cogauge is introduced. It is shown that this class of functions can be considered as an extension of the class of so-called min-type functions in normed linear spaces. We deduce that a plus-cogauge is superlinear and continuous, if and only if it is superlinear on the normed space $$X$$ X and linear on a nontrivial subspace of $$X$$ X . A cone separation theorem for closed radiant sets is obtained, which plays a key role in solving large-scale knowledge-based data classification problems. We shall also identify $$n$$ n -linear independent vectors in the Euclidean space to separate a closed radiant set from a point, which does not belong to the set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0584-9
    DOI: 10.1007/s10957-014-0584-9
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    References listed on IDEAS

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    4. 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.
    5. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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