Minimum Type Functions, Plus-Cogauges, and Applications

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.