# 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.

Type
Publication
Mathematical Programming B
Date
Tags
Links
Citation
T. G. Kolda. Numerical Optimization for Symmetric Tensor Decomposition. Mathematical Programming B, Vol. 151, No. 1, pp. 225-248, 2015. https://doi.org/10.1007/s10107-015-0895-0

### Keywords

symmetric, outer product, canonical polyadic, tensor decomposition, completely positive, nonnegative

### BibTeX

@article{Ko15,
author = {Tamara G. Kolda},
title = {Numerical Optimization for Symmetric Tensor Decomposition},
journal = {Mathematical Programming B},
volume = {151},
number = {1},
pages = {225-248},
month = {April},
year = {2015},
doi = {10.1007/s10107-015-0895-0},
eprint = {1410.4536},
}