Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
A real generalized trisecant trichotomy
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Algorithm for low-rank decomposition of partially symmetric tensors via flattening orthogonalization and shifted power method with global convergence proof.
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Multi-subspace power method for decomposing partially symmetric tensors
Algorithm for low-rank decomposition of partially symmetric tensors via flattening orthogonalization and shifted power method with global convergence proof.