Considering copositivity locally
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1969 | |
dc.contributor.author | Dickinson, Peter J.C. | |
dc.contributor.author | Hildebrand, Roland | |
dc.date.accessioned | 2016-03-24T17:37:12Z | |
dc.date.available | 2019-06-28T08:14:59Z | |
dc.date.issued | 2014 | |
dc.description.abstract | Let $A$ be an element of the copositive cone $coposn$. A zero $vu$ of $A$ is a nonnegative vector whose elements sum up to one and such that $vu^TAvu = 0$. The support of $vu$ is the index set $Suppvu subset 1,dots,n$ corresponding to the nonzero entries of $vu$. A zero $vu$ of $A$ is called minimal if there does not exist another zero $vv$ of $A$ such that its support $Suppvv$ is a strict subset of $Suppvu$. Our main result is a characterization of the cone of feasible directions at $A$, i.e., the convex cone $VarKA$ of real symmetric $n times n$ matrices $B$ such that there exists $delta > 0$ satisfying $A + delta B in coposn$. This cone is described by a set of linear inequalities on the elements of $B$ constructed from the set of zeros of $A$ and their supports. This characterization furnishes descriptions of the minimal face of $A$ in $coposn$, and of the minimal exposed face of $A$ in $coposn$, by sets of linear equalities and inequalities constructed from the set of minimal zeros of $A$ and their supports. In particular, we can check whether $A$ lies on an extreme ray of $coposn$ by examining the solution set of a system of linear equations. In addition, we deduce a simple necessary and sufficient condition on the irreducibility of $A$ with respect to a copositive matrix $C$. Here $A$ is called irreducible with respect to $C$ if for all $delta > 0$ we have $A - delta C notin coposn$. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2144 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/3000 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | Copositive matrix | eng |
dc.subject.other | face | eng |
dc.subject.other | irreducibility | eng |
dc.subject.other | extreme rays | eng |
dc.title | Considering copositivity locally | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- 798208406.pdf
- Size:
- 173.35 KB
- Format:
- Adobe Portable Document Format
- Description: