sublinear function

Epigraphical cones I

  • Alberto Seeger
    • Categories Linear, Cone and Semidefinite Programming Tags , , , , , ,

    Up to orthogonal transformation, a solid closed convex cone $K$ in the Euclidean space $\mathbb{R}^{n+1}$ is the epigraph of a nonnegative sublinear function $f:\mathbb{R}^n\to \mathbb{R}$. This work explores the link between the geometric properties of $K$ and the analytic properties of $f$. CitationJOURNAL OF CONVEX ANALYSIS, 2011, in press. ArticleDownload View PDF

    Epigraphical cones II

  • Alberto Seeger
    • Categories Linear, Cone and Semidefinite Programming Tags , , , , , ,

    This is the second part of a work devoted to the theory of epigraphical cones and their applications. A convex cone $K$ in the Euclidean space $\mathbb{R}^{n+1}$ is an epigraphical cone if it can be represented as epigraph of a nonnegative sublinear function $f: \mathbb{R}^n\to \mathbb{R}$. We explore the link between the geometric properties of … Read more