Mathematical Programming

, Volume 99, Issue 2, pp 283–296

Safe bounds in linear and mixed-integer linear programming


DOI: 10.1007/s10107-003-0433-3

Cite this article as:
Neumaier, A. & Shcherbina, O. Math. Program., Ser. A (2004) 99: 283. doi:10.1007/s10107-003-0433-3


Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic, cheap pre- and postprocessing of the linear programs arising in a branch-and-cut framework can guarantee that no solution is lost, at least for mixed-integer programs in which all variables can be bounded rigorously by bounds of reasonable size.


linear programmingmixed-integer programmingrounding errorsdirected roundinginterval arithmeticbranch-and-cutlower boundsmixed-integer roundinggeneralized Gomory cutsafe cutssafe presolvecertificate of infeasibility

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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Institut für MathematikUniversität WienWienAustria