Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial
  Optimization Problems with Binary, Box and Complementarity Constraints   The software package BBCPOP is a MATLAB implementation of a hierarchy of
sparse doubly nonnegative (DNN) relaxations of a class of polynomial
optimization (minimization) problems (POPs) with binary, box and
complementarity (BBC) constraints. Given a POP in the class and a relaxation
order, BBCPOP constructs a simple conic optimization problem (COP), which
serves as a DNN relaxation of the POP, and then solves the COP by applying the
bisection and projection (BP) method. The COP is expressed with a linear
objective function and constraints described as a single hyperplane and two
cones, which are the Cartesian product of positive semidefinite cones and a
polyhedral cone induced from the BBC constraints. BBCPOP aims to compute a
tight lower bound for the optimal value of a large-scale POP in the class that
is beyond the comfort zone of existing software packages. The robustness,
reliability and efficiency of BBCPOP are demonstrated in comparison to the
state-of-the-art software SDP package SDPNAL+ on randomly generated sparse POPs
of degree 2 and 3 with up to a few thousands variables, and ones of degree 4,
5, 6. and 8 with up to a few hundred variables. Comparison with other BBC POPs
that arise from combinatorial optimization problems such as quadratic
assignment problems are also reported. The software package BBCPOP is available
at https://sites.google.com/site/bbcpop1/.

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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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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: adap-org
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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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: math-ph
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The categories of this paper are: econ