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Andrei Afonin (afonin.adphystech.edu) Abstract: We provide a complete classification of the extreme rays of the $6 \times 6$ copositive cone ${\cal COP}^6$. We proceed via a coarse intermediate classification of the possible minimal zero support set of an exceptional extremal matrix $A \in {\cal COP}^6$. To each such minimal zero support set we construct a stratified semialgebraic manifold in the space of real symmetric $6 \times 6$ matrices ${\cal S}^6$, parameterized in a semitrigonometric way, which consists of all exceptional extremal matrices $A \in {\cal COP}^6$ having this minimal zero support set. Each semialgebraic stratum is characterized by the supports of the minimal zeros $u$ as well as the supports of the corresponding matrixvector products $Au$. The analysis uses recently and newly developed methods that are applicable also to copositive matrices of arbitrary order. Keywords: copositive matrix, extreme ray, minimal zero, nonconvex optimization Category 1: Linear, Cone and Semidefinite Programming (Other ) Category 2: Global Optimization (Theory ) Citation: Download: [PDF] Entry Submitted: 11/22/2019 Modify/Update this entry  
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