Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Accelerated Newton-Dinkelbach Method and its Application to Two
  Variables Per Inequality Systems   We present an accelerated, or 'look-ahead' version of the Newton-Dinkelbach
method, a well-known technique for solving fractional and parametric
optimization problems. This acceleration halves the Bregman divergence between
the current iterate and the optimal solution within every two iterations. Using
the Bregman divergence as a potential in conjunction with combinatorial
arguments, we obtain strongly polynomial algorithms in three applications
domains: (i) For linear fractional combinatorial optimization, we show a
convergence bound of $O(m \log m)$ iterations; the previous best bound was
$O(m^2 \log m)$ by Wang et al. (2006). (ii) We obtain a strongly polynomial
label-correcting algorithm for solving linear feasibility systems with two
variables per inequality (2VPI). For a 2VPI system with $n$ variables and $m$
constraints, our algorithm runs in $O(mn)$ iterations. Every iteration takes
$O(mn)$ time for general 2VPI systems, and $O(m + n \log n)$ time for the
special case of deterministic Markov Decision Processes (DMDPs). This extends
and strengthens a previous result by Madani (2002) that showed a weakly
polynomial bound for a variant of the Newton-Dinkelbach method for solving
DMDPs. (iii) We give a simplified variant of the parametric submodular function
minimization result by Goemans et al. (2017).

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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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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: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat