Structural properties of faces of the cone of copositive matrices
| Autor: | Tatiana Tchemisova, Olga Kostyukova |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
General Mathematics Completely positive matrices completely positive matrices copositive cone Zero (complex analysis) Structure (category theory) Mathematics::Optimization and Control Copositive matrices Minimal exposed cone Mathematics::Spectral Theory Cone (formal languages) Copositive cone Face (geometry) minimal exposed cone QA1-939 Computer Science (miscellaneous) copositive matrices Engineering (miscellaneous) Mathematics Subspace topology |
| Zdroj: | Mathematics, Vol 9, Iss 2698, p 2698 (2021) Mathematics Volume 9 Issue 21 |
| Popis: | In this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, we obtain several explicit representations of faces of the copositive cone and compare them. Given a face of the cone of copositive matrices, we describe the subspace generated by that face and the minimal exposed face containing it. Summarizing the results obtained in the paper, we systematically show what information can be extracted about the given copositive face in the case of incomplete data. Several examples for illustrating the main findings of the paper and also for justifying the usefulness of the developed approach to the study of the facial structure of the copositive cone are discussed. |
| Databáze: | OpenAIRE |
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