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Error bounds for mixed integer linear optimization problems

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Abstract

We introduce computable a priori and a posteriori error bounds for optimality and feasibility of a point generated as the rounding of an optimal point of the LP relaxation of a mixed integer linear optimization problem. Treating the mesh size of integer vectors as a parameter allows us to study the effect of different “granularities” in the discrete variables on the error bounds. Our analysis mainly bases on a global error bound for mixed integer linear problems constructed via a so-called grid relaxation retract. Relations to proximity results, the integer rounding property, and binary analytic problems are highlighted.

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Acknowledgments

The author is grateful to the anonymous referees for their precise and substantial remarks, and to Immanuel Bomze, Peter Gritzmann and Guoyin Li for helpful comments on an earlier version of this manuscript.

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  1. Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

    Oliver Stein

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  1. Oliver Stein
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Correspondence to Oliver Stein.

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Stein, O. Error bounds for mixed integer linear optimization problems. Math. Program. 156, 101–123 (2016). https://doi.org/10.1007/s10107-015-0872-7

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  • DOI: https://doi.org/10.1007/s10107-015-0872-7

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