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Title: Numerical optimization for symmetric tensor decomposition

Abstract

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.

Authors:
 [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1497638
Report Number(s):
SAND2014-18405J
Journal ID: ISSN 0025-5610; 672377
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Mathematical Programming
Additional Journal Information:
Journal Volume: 151; Journal Issue: 1; Journal ID: ISSN 0025-5610
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Kolda, Tamara G. Numerical optimization for symmetric tensor decomposition. United States: N. p., 2015. Web. doi:10.1007/s10107-015-0895-0.
Kolda, Tamara G. Numerical optimization for symmetric tensor decomposition. United States. doi:10.1007/s10107-015-0895-0.
Kolda, Tamara G. Sat . "Numerical optimization for symmetric tensor decomposition". United States. doi:10.1007/s10107-015-0895-0. https://www.osti.gov/servlets/purl/1497638.
@article{osti_1497638,
title = {Numerical optimization for symmetric tensor decomposition},
author = {Kolda, Tamara G.},
abstractNote = {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.},
doi = {10.1007/s10107-015-0895-0},
journal = {Mathematical Programming},
number = 1,
volume = 151,
place = {United States},
year = {2015},
month = {4}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 15 works
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Figures / Tables:

Table 1 Table 1: Index and monomial representations for $\mathbb{S}^{[3,2]}$.

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