Self-dual cones in euclidean spaces

Abstract

Listen

Translate article

Self-dual convex cones arise, for example, in the study of copositive matrices and copositive quadratic forms. We begin by giving necessary and sufficient conditions for a cone to be the orthogonal transform of the positive orthant. Next we give a technique for constructing self-dual cones in E n which produces for all n≥3 many self-dual cones and even polyhedral self-dual cones which are not similar to the nonnegative orthant. We examine the structure of self-dual cones in E n which contain an n - 1 dimensional self-dual cone. Finally we show that if K is a cone which is contained in its dual, then there is a self-dual cone containing K.