## Copositivity and Complete Positivity

 dc.date.accessioned 2019-10-24T15:37:26Z dc.date.available 2019-10-24T15:37:26Z dc.date.issued 2017 dc.identifier.uri http://publications.mfo.de/handle/mfo/3616 dc.description.abstract A real matrix $A$ is called copositive if $x^TAx \ge 0$ holds for all $x \in \mathbb R^n_+$. A matrix $A$ is called completely positive if it can be factorized as $A = BB^T$ , where $B$ is an entrywise nonnegative matrix. The concept of copositivity can be traced back to Theodore Motzkin in 1952, and that of complete positivity to Marshal Hall Jr. in 1958. The two classes are related, and both have received considerable attention in the linear algebra community and in the last two decades also in the mathematical optimization community. These matrix classes have important applications in various fields, in which they arise naturally, including mathematical modeling, optimization, dynamical systems and statistics. More applications constantly arise. The workshop brought together people working in various disciplines related to copositivity and complete positivity, in order to discuss these concepts from different viewpoints and to join forces to better understand these difficult but fascinating classes of matrices. dc.title Copositivity and Complete Positivity 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. de 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. en dc.identifier.doi 10.14760/OWR-2017-52 local.series.id OWR-2017-52 local.subject.msc 37 local.subject.msc 90 local.subject.msc 15 local.subject.msc 93 local.sortindex 1056 local.date-range 29 Oct - 04 Nov 2017 local.workshopcode 1744b local.workshoptitle Copositivity and Complete Positivity local.organizers Abraham Berman, Haifa; Immanuel M. Bomze, Vienna; Mirjam Dür, Trier; Naomi Shaked-Monderer, Yezreel Valley local.report-name Workshop Report 2017,52 local.opc-photo-id 1744b local.publishers-doi 10.4171/OWR/2017/52 local.ems-reference Berman Abraham, Bomze Immanuel, Dür Mirjam, Shaked-Monderer Naomi: Copositivity and Complete Positivity. Oberwolfach Rep. 14 (2017), 3071-3120. doi: 10.4171/OWR/2017/52
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