Minimal representation of convex polyhedral sets

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A system of linear inequality and equality constraints determines a convex polyhedral set of feasible solutions S. We consider the relation of all individual constraints to S, paying special attention to redundancy and implicit equalities. The main theorem derived here states that the total number of constraints together determining S 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.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalJournal of optimization theory and applications
Issue number1
Publication statusPublished - 1 Sep 1982


  • Linear equalities
  • Linear inequalities
  • Minimal representation
  • Systems of linear constraints

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