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Strong IP Formulations Need Large Coefficients

Christopher Hojny (hojny***at***mathematik.tu-darmstadt.de)

Abstract: The development of practically well-behaving integer programming formulations is an important aspect of solving linear optimization problems over a set $X \subseteq \{0,1\}^n$. In practice, one is often interested in strong integer formulations with additional properties, e.g., bounded coefficients to avoid numerical instabilities. This article presents a lower bound on the size of coefficients in any strong integer formulation of $X$ and demonstrates that certain integer sets $X$ require exponentially large coefficients in any strong integer formulation. We also characterize the minimum size of an integer formulation of $X \subseteq \{0,1\}^n$ with bounded coefficients.

Keywords: integer Programming, IP formulation, bounded coefficients, strong cutting planes

Category 1: Integer Programming

Category 2: Integer Programming (0-1 Programming )


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Entry Submitted: 11/20/2018
Entry Accepted: 11/20/2018
Entry Last Modified: 12/10/2018

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