Gramian Tensor Decomposition via Semidefinite Programming

Erik Skau; Agnes Szanto

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arXiv · 1708.02659

Gramian Tensor Decomposition via Semidefinite Programming

Erik Skau·Agnes Szanto

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Abstract

In this paper we examine a symmetric tensor decomposition problem, the Gramian decomposition, posed as a rank minimization problem. We study the relaxation of the problem and consider cases when the relaxed solution is a solution to the original problem. In some instances of tensor rank and order, we prove generically that the solution to the relaxation will be optimal in the original. In other cases, we present interesting examples and approaches that demonstrate the intricacy of this problem.

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Erik Skau, Agnes Szanto. 2017-08-08. Gramian Tensor Decomposition via Semidefinite Programming. https://arxiv.org/abs/1708.02659

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