Minimum Type Functions, Plus-Cogauges, and Applications

A. R. Doagooei ()
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A. R. Doagooei: Shahid Bahonar University of Kerman

Journal of Optimization Theory and Applications, 2015, vol. 164, issue 2, No 9, 564 pages

Abstract: 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.

Keywords: Global optimization; Min-type function; Plus-Minkowski gauge; Radiant set; Separation theorems; 26B25; 49N15; 90C46 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0584-9

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