Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Ordered Weighted $\ell_1$ Norm: Atomic Formulation, Projections, and
  Algorithms   The ordered weighted $\ell_1$ norm (OWL) was recently proposed, with two
different motivations: its good statistical properties as a sparsity promoting
regularizer; the fact that it generalizes the so-called {\it octagonal
shrinkage and clustering algorithm for regression} (OSCAR), which has the
ability to cluster/group regression variables that are highly correlated. This
paper contains several contributions to the study and application of OWL
regularization: the derivation of the atomic formulation of the OWL norm; the
derivation of the dual of the OWL norm, based on its atomic formulation; a new
and simpler derivation of the proximity operator of the OWL norm; an efficient
scheme to compute the Euclidean projection onto an OWL ball; the instantiation
of the conditional gradient (CG, also known as Frank-Wolfe) algorithm for
linear regression problems under OWL regularization; the instantiation of
accelerated projected gradient algorithms for the same class of problems.
Finally, a set of experiments give evidence that accelerated projected gradient
algorithms are considerably faster than CG, for the class of problems
considered.

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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
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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: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat