Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the derivative cones of polyhedral cones   Hyperbolic polynomials elegantly encode a rich class of convex cones that
includes polyhedral and spectrahedral cones. Hyperbolic polynomials are closed
under taking polars and the corresponding cones, the derivative cones, yield
relaxations for the associated optimization problem and exhibit interesting
facial properties. While it is unknown if every hyperbolicity cone is a section
of the positive semidefinite cone, it is natural to ask whether spectrahedral
cones are closed under taking polars. In this note we give an affirmative
answer for polyhedral cones by exhibiting an explicit spectrahedral
representation for the first derivative cone. We also proof that higher polars
do not have an determinantal representation which shows that the problem for
general spectrahedral cones is considerably more difficult.

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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess