Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: T-positive semidefiniteness of third-order symmetric tensors and
  T-semidefinite programming   The T-product for third-order tensors has been used extensively in the
literature. In this paper, we first introduce the first-order and second-order
T-derivatives for the multi-vector real-valued function with the tensor
T-product; and inspired by an equivalent characterization of a twice
continuously T-differentiable multi-vector real-valued function being convex,
we present a definition of the T-positive semidefiniteness of third-order
symmetric tensors. After that, we extend many properties of positive
semidefinite matrices to the case of third-order symmetric tensors. In
particular, analogue to the widely used semidefinite programming (SDP for
short), we introduce the semidefinite programming over the third-order
symmetric tensor space (T-semidefinite programming or TSDP for short), and
provide a way to solve the TSDP problem by converting it into an SDP problem in
the complex domain. Furthermore, we give several examples which can be
formulated (or relaxed) as TSDP problems, and report preliminary numerical
results for two unconstrained polynomial optimization problems. Experiments
show that finding the global minimums of polynomials via the TSDP relaxation
outperforms the traditional SDP relaxation for the test examples.

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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph