Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Balas formulation for the union of polytopes is optimal   A celebrated theorem of Balas gives a linear mixed-integer formulation for
the union of two nonempty polytopes whose relaxation gives the convex hull of
this union. The number of inequalities in Balas formulation is linear in the
number of inequalities that describe the two polytopes and the number of
variables is doubled. In this paper we show that this is best possible: in
every dimension there exist two nonempty polytopes such that if a formulation
for the convex hull of their union has a number of inequalities that is
polynomial in the number of inequalities that describe the two polytopes, then
the number of additional variables is at least linear in the dimension of the
polytopes. We then show that this result essentially carries over if one wants
to approximate the convex hull of the union of two polytopes and also in the
more restrictive setting of lift-and-project.

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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th