Abstract
Given an inconsistent set of inequalities Ax ⩽b, theirreducible inconsistent subsystems (IISs) designate subsets of the inequalities such that at least one member of each subset must be deleted in order to achieve a feasible system. By solving a set covering problem over the IISs, one can determine a minimum weight set of inequalities that must be deleted in order to achieve feasibility. Since the number of IISs is generally exponential in the size of the original subsystem, we generate the IISs only when they are violated by a trial solution. Computational results on the NETLIB infeasible LP library are given.
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This author was supported by Air Force Office of Scientific Research and Office of Naval Research Contract #F49620-92-J-0248-DEF.
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Parker, M., Ryan, J. Finding the minimum weight IIS cover of an infeasible system of linear inequalities. Ann Math Artif Intell 17, 107–126 (1996). https://doi.org/10.1007/BF02284626
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DOI: https://doi.org/10.1007/BF02284626