Abstract
We show that a consistency check of a linear system of inequalitiesAx≤b reduces to check whetherQb≥0 for a certain matrixQ. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values ofb, one need not run a numerical algorithm for eachb.
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Communicated by D. G. Luenberger
On leave at the Electronics Research Laboratory of the University of California at Berkeley in a CNRS/NSF Exchange Program.
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Lasserre, J.B. Consistency of a linear system of inequalities. J Optim Theory Appl 49, 177–179 (1986). https://doi.org/10.1007/BF00939253
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DOI: https://doi.org/10.1007/BF00939253