Dehomogenization for completely positive tensors
نویسندگان
چکیده
A real symmetric tensor is completely positive (CP) if it a sum of powers nonnegative vectors. We propose dehomogenization approach for studying CP tensors. This gives new Moment-SOS relaxations Detection tensors and the linear conic optimization with cones can be solved more efficiently by approach.
منابع مشابه
Completely Positive Tensors: Properties, Easily Checkable Subclasses, and Tractable Relaxations
The completely positive (CP) tensor verification and decomposition are essential in tensor analysis and computation due to the wide applications in statistics, computer vision, exploratory multiway data analysis, blind source separation, and polynomial optimization. However, it is generally NP-hard as we know from its matrix case. To facilitate the CP tensor verification and decomposition, more...
متن کاملNonnegative Tensor Factorization, Completely Positive Tensors, and a Hierarchical Elimination Algorithm
Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has an exact symmetric nonnegative factorization, is called a completely positive tensor. This concept extends the concept of completely positive matrices. A classical result in the theory of completely positive m...
متن کاملEssentially Positive Tensors
The Perron-Frobenius Theorem for irreducible higher order tensors does not guarantee simplicity of the unique positive eigenvalue nor does it guarantee the unique positive eigenvalue is strictly larger than the modulus of any other eigenvalue. Irreducibility of a tensor in relation to a graph is studied. A higher order tensor is essentially positive if it takes the positive cone to its interior...
متن کاملCompletely positive quantum dissipation
A completely positive master equation describing quantum dissipation for a Brownian particle is derived starting from microphysical collisions, exploiting a recently introduced approach to subdynamics of a macrosystem. The obtained equation can be cast into Lindblad form with a single generator for each Cartesian direction. Temperature dependent friction and diffusion coefficients for both posi...
متن کاملCompletely Positive Semidefinite Rank
An n×n matrix X is called completely positive semidefinite (cpsd) if there exist d×d Hermitian positive semidefinite matrices {Pi}i=1 (for some d ≥ 1) such that Xij = Tr(PiPj), for all i, j ∈ {1, . . . , n}. The cpsd-rank of a cpsd matrix is the smallest d ≥ 1 for which such a representation is possible. In this work we initiate the study of the cpsd-rank which we motivate twofold. First, the c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerical Algebra, Control and Optimization
سال: 2023
ISSN: ['2155-3297', '2155-3289']
DOI: https://doi.org/10.3934/naco.2022037