Applications to Discrete Problems

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


In Chapters 2 and 3 we have presented a general theoretical framework for generating a hierarchy of relaxations spanning the spectrum from the continuous linear programming relaxation to the convex hull representation. In practice, the actual relaxation adopted needs to be carefully designed using these general concepts and results as guidelines, being specialized for the particular application. Often, even a full first-level relaxation might be too large to manage computationally, although this is highly dependent on linear programming technology. For example, as mentioned in Section 2.5, first as well as second-level relaxations have been successfully implemented for the notorious quadratic assignment problem, despite their massive size; such problems have as many as 15–25 facilities and location sites.


Travel Salesman Problem Quadratic Programming Problem Quadratic Assignment Problem Logical Test Incumbent Solution 
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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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