Geodesic
Non-exposed faces of the cone of completely positive matrices
Trudy Instituta matematiki, Tome 32 (2024) no. 2, pp. 56-68

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In this paper, we consider the cone of completely positive matrices. Currently, some families of non-exposed polyhedral faces of this cone were constructed. Inspired by these results, in this paper, we continue the study of the existence and properties of non-exposed faces of the cone of completely positive matrices. We prove a criterion for a face of this cone to be non-exposed. We also provide sufficient conditions that can be easily checked numerically. We show that for any $p\geqslant 6$, there exist non-exposed non-polyhedral faces of the cone of $p\times p$ completely positive matrices. Illustrative examples are given.
Keywords: conic optimization, completely positive matrices, $K$-semidefinite matrices, a face of a cone, exposed and non-exposed faces of a cone. 
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     author = {O. I. Kostyukova},
     title = {Non-exposed faces of the cone of completely positive matrices},
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     url = {http://geodesic.mathdoc.fr/item/TIMB_2024_32_2_a4/}
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O. I. Kostyukova. Non-exposed faces of the cone of completely positive matrices. Trudy Instituta matematiki, Tome 32 (2024) no. 2, pp. 56-68. http://geodesic.mathdoc.fr/item/TIMB_2024_32_2_a4/