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 \(X\) and linear on a nontrivial subspace of \(X\). 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 \(n\)-linear independent vectors in the Euclidean space to separate a closed radiant set from a point, which does not belong to the set.
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The author thanks the anonymous referees and the editor for their valuable comments, which improved the presentation of the paper significantly.
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Doagooei, A.R. Minimum Type Functions, Plus-Cogauges, and Applications. J Optim Theory Appl 164, 551–564 (2015). https://doi.org/10.1007/s10957-014-0584-9
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DOI: https://doi.org/10.1007/s10957-014-0584-9