Completely Positive Tensors: Properties, Easily Checkable Subclasses, and Tractable Relaxations

DOI10.1137/15M1025220zbMath1349.15026OpenAlexW2552988668MaRDI QIDQ2834695

Liqun Qi, Ziyan Luo

Publication date: 23 November 2016

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1025220

zbMATH Keywords

completely positive tensorssum-of-squares tensorscompletely positive Vandermonde decompositiondoubly nonnegative tensorsLehmer tensorspositive Cauchy tensors

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Multilinear algebra, tensor calculus (15A69)

Related Items (18)

Completely positive tensor recovery with minimal nuclear value ⋮ \(\mathrm{P}\)-tensors, \(\mathrm{P}_0\)-tensors, and their applications ⋮ High-order sum-of-squares structured tensors: theory and applications ⋮ Multiplicative algorithms for symmetric nonnegative tensor factorizations and its applications ⋮ Dehomogenization for completely positive tensors ⋮ Completely Positive Binary Tensors ⋮ Completely positive tensors in the complex field ⋮ Copositive tensor optimization problem and its applications to hypergraphs ⋮ HIGH-ORDER COPOSITIVE TENSORS AND ITS APPLICATIONS ⋮ Geometry of the Copositive Tensor Cone and its Dual ⋮ Positive definite and Gram tensor complementarity problems ⋮ Copositive tensor detection and its applications in physics and hypergraphs ⋮ A hierarchy of semidefinite relaxations for completely positive tensor optimization problems ⋮ On \(\{0,1\}\) CP tensors and CP pseudographs ⋮ A homotopy method for solving multilinear systems with strong completely positive tensors ⋮ A semidefinite relaxation algorithm for checking completely positive separable matrices ⋮ Some results on the Hadamard product of tensors ⋮ A new class of positive semi-definite tensors

Uses Software

• testmatrix

Cites Work

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