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, for problems with low-rank structure. 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.

References in corpus (4)

• An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs
• Completely positive tensor decomposition
• Generating Polynomials and Symmetric Tensor Decompositions
• All Real Eigenvalues of Symmetric Tensors

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