Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Method for Quickly Bounding the Optimal Objective Value of an OPF
  Problem using a Semidefinite Relaxation and a Local Solution   Optimal power flow (OPF) is an important problem in the operation of electric
power systems. Due to the OPF problem's non-convexity, there may exist multiple
local optima. Certifiably obtaining the global solution is important for
certain applications of OPF problems. Many global optimization techniques
compute an optimality gap that compares the achievable objective value
corresponding to the feasible point from a local solution algorithm with the
objective value bound from a convex relaxation technique. Rather than the
traditional practice of completely separating the local solution and convex
relaxation computations, this paper proposes a method that exploits information
from a local solution to speed the computation of an objective value bound
using a semidefinite programming (SDP) relaxation. The improvement in
computational tractability comes with the trade-off of reduced tightness for
the resulting objective value bound. Numerical experiments illustrate this
trade-off, with the proposed method being faster but weaker than the SDP
relaxation and slower but tighter than second-order cone programming (SOCP) and
quadratic convex (QC) relaxations for many large test cases.

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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an