On the duality operator of a convex cone
type: Item
instance of: scholarly article
title: On the duality operator of a convex cone
zbMATH Open document ID: 0553.52006
DOI: 10.1016/0024-3795(85)90265-4
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
review text: Convex cones in the euclidean space \(R^ n\) are considered, and properties of the duality operator \(d_ K\) are studied not only for so called proper cones K, but also for general ones. Several propositions are proved concerning face lattices of convex sets and cones. The main results say in which cases, for K closed, the operator \(d_ K\) is injective (surjective). Some sufficient conditions are given for a cone to be the point's cone (at the origin) of a compact convex set.
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 3881396
zbMATH Keywords: Convex cones
zbMATH Keywords: duality operator
zbMATH Keywords: face lattices
zbMATH Keywords: convex sets
zbMATH Keywords: point's cone
author: Bit-Shun Tam
reviewed by: Jānis Cīrulis
MaRDI profile type: Publication
full work available at URL: 0024-3795(85)90265-4
OpenAlex ID: W2065056910
cites work: The lattice of faces of a finite dimensional cone
cites work: Faces and duality in convex cones
cites work: Perfect cones
cites work: Modular face lattices: Low dimensional cases
cites work: Theory of cones
cites work: Cones, matrices and mathematical programming
cites work: Q5331549
cites work: Q4056047
cites work: Q5638112
cites work: Cross-Positive Matrices
cites work: Some results of polyhedral cones and simplicial cones
cites work: On the semiring of cone preserving maps
cites work: Arcwise Convex Sets
cites work: On point classification in convex sets.
description: scientific article; zbMATH DE number 3881396