Abstract
A system of linear inequality and equality constraints determines a convex polyhedral set of feasible solutionsS. We consider the relation of all individual constraints toS, paying special attention to redundancy and implicit equalities. The main theorem derived here states that the total number of constraints together determiningS is minimal if and only if the system contains no redundant constraints and/or implicit equalities. It is shown that the existing theory on the representation of convex polyhedral sets is a special case of the theory developed here.
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Additional information
Communicated by O. L. Mangasarian
The author is indebted to Dr. A. C. F. Vorst (Erasmus University, Rotterdam, Holland) for stimulating discussions and comments, which led to considerable improvements in many proofs. Most of the material in this paper originally appeared in the author's dissertation (Ref. 1). The present form was prepared with partial support from a NATO Science Fellowship for the Netherlands Organization for the Advancement of Pure Research (ZWO) and a CORE Research Fellowship.
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Telgen, J. Minimal representation of convex polyhedral sets. J Optim Theory Appl 38, 1–24 (1982). https://doi.org/10.1007/BF00934319
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DOI: https://doi.org/10.1007/BF00934319