Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nondegeneracy and Inexactness of Semidefinite Relaxations of Optimal
  Power Flow   The Optimal Power Flow (OPF) problem can be reformulated as a nonconvex
Quadratically Constrained Quadratic Program (QCQP). There is a growing body of
work on the use of semidefinite programming relaxations to solve OPF. The
relaxation is exact if and only if the corresponding optimal solution set
contains a rank-one matrix. In this paper, we establish sufficient conditions
guaranteeing the nonexistence of a rank-one matrix in said optimal solution
set. In particular, we show that under mild assumptions on problem
nondegeneracy, any optimal solution to the semidefinite relaxation will have
rank greater than one, if the number of equality and active inequality
constraints is at least twice the number of buses in the network. The
sufficient condition holds for arbitrary network topologies (including tree
networks). We empirically evaluate the practical implications of these results
on several test cases from the literature.

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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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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: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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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: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci