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Title: Numerical optimization for symmetric tensor decomposition

Journal Article · · Mathematical Programming
 [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on real-valued decompositions, both unconstrained and nonnegative. We discuss when solutions exist and how to formulate the mathematical program. Numerical results show the properties of the proposed formulations (including one that ignores symmetry) on a set of test problems and illustrate that these straightforward formulations can be effective even though the problem is nonconvex.

Research Organization:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1497638
Report Number(s):
SAND2014-18405J; 672377
Journal Information:
Mathematical Programming, Vol. 151, Issue 1; ISSN 0025-5610
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 31 works
Citation information provided by
Web of Science

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Cited By (13)

Copositive tensor detection and its applications in physics and hypergraphs journal August 2017
Completely positive tensor recovery with minimal nuclear value journal April 2018
The sparsest solutions to Z-tensor complementarity problems journal February 2016
Validating quantum-classical programming models with tensor network simulations journal December 2018
The Sparsest Solutions to $Z$-Tensor Complementarity Problems preprint January 2015
Joint Embedding of Graphs journal April 2021
Low Rank Symmetric Tensor Approximations journal January 2017
Completely Positive Tensors and Multi-Hypergraphs preprint January 2015
On {0,1} CP Tensors and CP Multi-hypergraphs preprint January 2016
Validating Quantum-Classical Programming Models with Tensor Network Simulations text January 2018
Subspace power method for symmetric tensor decomposition and generalized PCA preprint January 2019
Symmetry Breaking in Symmetric Tensor Decomposition preprint January 2021
Separable symmetric tensors and separable anti-symmetric tensors preprint January 2022

Figures / Tables (10)


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