Abstract
A symmetric matrix A is completely positive (CP) if there exists an entrywise nonnegative matrix B such that \(A = BB^T\). We characterize the interior of the CP cone. A semidefinite algorithm is proposed for checking whether a matrix is in the interior of the CP cone, and its properties are studied. A CP-decomposition of a matrix in Dickinson’s form can be obtained if it is an interior of the CP cone. Some computational experiments are also presented.
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The authors are grateful to the referees for their valuable and constructive comments and advices, especially for suggesting Theorem 2.1 and some random examples, which have greatly improved the presentation of the paper.
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Jinyan Fan: The work is partially supported by NSFC 11171217.
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Zhou, A., Fan, J. Interiors of completely positive cones. J Glob Optim 63, 653–675 (2015). https://doi.org/10.1007/s10898-015-0309-0
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DOI: https://doi.org/10.1007/s10898-015-0309-0