RLT Hierarchy for General Discrete Mixed-Integer Problems

  • Hanif D. Sherali
  • Warren P. Adams
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 31)


Thus far, we have been focusing on 0–1 mixed-integer programming problems and have developed a general theory for generating a hierarchy of tight relaxations leading to the convex hull representation. However, in many applications, we encounter problems in which the decision variables are required to take on more general discrete or integer values as opposed to simply zero or one values. Of particular interest in this context are classes of problems involving variables that are restricted to taken on only a few discrete values, that are possibly not even consecutive integers, for which one might expect to have weak ordinary linear programming relaxations. In this chapter, we demonstrate how one can generate a hierarchy of relaxations leading to the convex hull representation for such general bounded variable discrete optimization problems.


Valid Inequality Redundant Constraint Distinct Index Original Constraint Tight Relaxation 
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Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Hanif D. Sherali
    • 1
  • Warren P. Adams
    • 2
  1. 1.Department of Industrial and Systems EngineeringVirginia Polytechnic Institute and State UniversityBlacksburgUSA
  2. 2.Department of Mathematical SciencesClemson UniversityClemsonUSA

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