Abstract:
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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