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Universität Augsburg
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Universität Augsburg
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Herr Alexander Oertel
Universität Rostock
spricht am
Dienstag, 10. Februar 2026
um
10:00 Uhr
im
Raum 1009 (L1)
über das Thema:
| Abstract: |
| Voronoi's classical theory of perfect matrices allows solving the sphere packing problem in lattices. This theory can be extended to the dual pair of completely positive and copositive matrices, that is to symmetric matrices of the form BB^T for a nonnegative matrix B and to symmetric matrices Q satisfying x^T Q x >= 0 for all nonnegative vectors x. This leads to a theory of perfect copositive matrices along with both outer and inner polyhedral approximations to the cone of completely positive matrices. They allow finding rational CP-certificates: For a rational completely positive matrix Q we find a rational nonnegative matrix B with Q=BB^T. If Q is not completely positive we also find a certificate for that. In this talk we summarize this theory. An important role plays the copositive minimum of a matrix Q, that is the minimum value of x^T Q x for nonnegative integral vectors x. We present the current strategies to solve the problem and introduce further ideas to solve it generally. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Mirjam Dür |