Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elementary polytopes with high lift-and-project ranks for strong
  positive semidefinite operators   We consider operators acting on convex subsets of the unit hypercube. These
operators are used in constructing convex relaxations of combinatorial
optimization problems presented as a 0,1 integer programming problem or a 0,1
polynomial optimization problem. Our focus is mostly on operators that, when
expressed as a lift-and-project operator, involve the use of semidefiniteness
constraints in the lifted space, including operators due to Lasserre and
variants of the Sherali--Adams and Bienstock--Zuckerberg operators. We study
the performance of these semidefinite-optimization-based lift-and-project
operators on some elementary polytopes --- hypercubes that are chipped (at
least one vertex of the hypercube removed by intersection with a closed
halfspace) or cropped (all $2^n$ vertices of the hypercube removed by
intersection with $2^n$ closed halfspaces) to varying degrees of severity
$\rho$. We prove bounds on $\rho$ where these operators would perform badly on
the aforementioned examples. We also show that the integrality gap of the
chipped hypercube is invariant under the application of several
lift-and-project operators of varying strengths.

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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th