Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Finite Optimal Convergence of Logic-Based Benders' Decomposition
  in Solving 0-1 Min-max Regret Optimization Problems with Interval Costs   This paper addresses a class of problems under interval data uncertainty
composed of min-max regret versions of classical 0-1 optimization problems with
interval costs. We refer to them as interval 0-1 min-max regret problems. The
state-of-the-art exact algorithms for this class of problems work by solving a
corresponding mixed integer linear programming formulation in a Benders'
decomposition fashion. Each of the possibly exponentially many Benders' cuts is
separated on the fly through the resolution of an instance of the classical 0-1
optimization problem counterpart. Since these separation subproblems may be
NP-hard, not all of them can be modeled by means of linear programming, unless
P = NP. In these cases, the convergence of the aforementioned algorithms are
not guaranteed in a straightforward manner. In fact, to the best of our
knowledge, their finite convergence has not been explicitly proved for any
interval 0-1 min-max regret problem. In this work, we formally describe these
algorithms through the definition of a logic-based Benders' decomposition
framework and prove their convergence to an optimal solution in a finite number
of iterations. As this framework is applicable to any interval 0-1 min-max
regret problem, its finite optimal convergence also holds in the cases where
the separation subproblems are NP-hard.

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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph