Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exposed faces of semidefinitely representable sets   A linear matrix inequality (LMI) is a condition stating that a symmetric
matrix whose entries are affine linear combinations of variables is positive
semidefinite. Motivated by the fact that diagonal LMIs define polyhedra, the
solution set of an LMI is called a spectrahedron. Linear images of spectrahedra
are called semidefinite representable sets. Part of the interest in
spectrahedra and semidefinite representable sets arises from the fact that one
can efficiently optimize linear functions on them by semidefinite programming,
like one can do on polyhedra by linear programming.
  It is known that every face of a spectrahedron is exposed. This is also true
in the general context of rigidly convex sets. We study the same question for
semidefinite representable sets. Lasserre proposed a moment matrix method to
construct semidefinite representations for certain sets. Our main result is
that this method can only work if all faces of the considered set are exposed.
This necessary condition complements sufficient conditions recently proved by
Lasserre, Helton and Nie.

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The categories of this paper are: cs
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The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex