Best Nonnegative Rank-One Approximations of Tensors
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Publication:5203971
DOI10.1137/18M1224064zbMath1454.90047arXiv1810.13372OpenAlexW2992276872WikidataQ114074276 ScholiaQ114074276MaRDI QIDQ5203971
Kim-Chuan Toh, Defeng Sun, Sheng-Long Hu
Publication date: 9 December 2019
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1810.13372
tensorpolynomialmultiformsdoubly nonnegative relaxation methoddoubly nonnegative semidefinite programnonnegative rank-1 approximation
Semidefinite programming (90C22) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69) Polynomial optimization (90C23)
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Cites Work
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- Tensor Decompositions and Applications
- Symmetric nonnegative tensors and copositive tensors
- Optimality conditions and finite convergence of Lasserre's hierarchy
- On the computational complexity of membership problems for the completely positive cone and its dual
- SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints
- Computing the polyadic decomposition of nonnegative third order tensors
- Nonnegative ranks, decompositions, and factorizations of nonnegative matrices
- Sum of squares methods for minimizing polynomial forms over spheres and hypersurfaces
- On the complexity of Putinar's Positivstellensatz
- Convergence rate analysis for the higher order power method in best rank one approximations of tensors
- Tensors of nonnegative rank two
- Completely positive reformulations for polynomial optimization
- Minimizing polynomials via sum of squares over the gradient ideal
- Global Optimization with Polynomials and the Problem of Moments
- Positive tensor factorization
- Lectures on Modern Convex Optimization
- On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
- Positive Maps and Separable Matrices
- Semidefinite Relaxations for Best Rank-1 Tensor Approximations
- Uniqueness of Nonnegative Tensor Approximations
- A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
- Tensor rank is NP-complete
- Shifted Power Method for Computing Tensor Eigenpairs
- Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
- On the Complexity of Nonnegative Matrix Factorization
- Some NP-complete problems in quadratic and nonlinear programming
- SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
- Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
- A Multilinear Singular Value Decomposition
- On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors
- Efficient Nonnegative Tucker Decompositions: Algorithms and Uniqueness
- A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization
- Tensor Decomposition for Signal Processing and Machine Learning
- A Complete Semidefinite Algorithm for Detecting Copositive Matrices and Tensors
- Solution of the truncated complex moment problem for flat data
- SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0)
- A Convergent 3-Block SemiProximal Alternating Direction Method of Multipliers for Conic Programming with 4-Type Constraints
- Maxima for Graphs and a New Proof of a Theorem of Turán
- Learning the parts of objects by non-negative matrix factorization
- Computing non-negative tensor factorizations
- A new bound for Pólya's theorem with applications to polynomials positive on polyhedra.
