Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-dual Smooth Approximations of Convex Functions via the Proximal
  Average   The proximal average of two convex functions has proven to be a useful tool
in convex analysis. In this note, we express Goebel's self-dual smoothing
operator in terms of the proximal average, which allows us to give a simple
proof of self duality. We also provide a novel self-dual smoothing operator.
Both operators are illustrated by smoothing the norm.

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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th