Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: SuperMann: a superlinearly convergent algorithm for finding fixed points
  of nonexpansive operators   Operator splitting techniques have recently gained popularity in convex
optimization problems arising in various control fields. Being fixed-point
iterations of nonexpansive operators, such methods suffer many well known
downsides, which include high sensitivity to ill conditioning and parameter
selection, and consequent low accuracy and robustness. As universal solution we
propose SuperMann, a Newton-type algorithm for finding fixed points of
nonexpansive operators. It generalizes the classical Krasnosel'skii-Mann
scheme, enjoys its favorable global convergence properties and requires exactly
the same oracle. It is based on a novel separating hyperplane projection
tailored for nonexpansive mappings which makes it possible to include steps
along any direction. In particular, when the directions satisfy a Dennis-Mor\'e
condition we show that SuperMann converges superlinearly under mild
assumptions, which, surprisingly, do not entail nonsingularity of the Jacobian
at the solution but merely metric subregularity. As a result, SuperMann
enhances and robustifies all operator splitting schemes for structured convex
optimization, overcoming their well known sensitivity to ill conditioning.

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The categories of this paper are: econ
37
The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: physics