Generalized Hierarchy for Exploiting Special Structures in Mixed-Integer Zero-One Problems

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


In the previous chapter, we discussed a technique for generating a hierarchy of relaxations that span the spectrum from the continuous LP relaxation to the convex hull of feasible solutions for linear mixed-integer 0–1 programming problems. The key construct was to compose a set of multiplication factors based on the bounding constraints 0 ≤ xe n on the binary variables x , and to use these factors to generate implied nonlinear product constraints, then tighten these constraints using the fact that x j 2 x j j = 1, …, n, and subsequently linearize the resulting polynomial problem through a variable substitution process. This process yielded tighter representations of the problem in higher dimensional spaces.


Travel Salesman Problem Valid Inequality Linear Programming Relaxation Product Constraint Conditional Logic 
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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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