Persistency in Discrete Optimization

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


Given a mixed 0–1 linear program in n binary variables, we studied in Chapter 2 the construction of an n + 1 level hierarchy of polyhedral approximations that ranges from the usual continuous relaxation at level 0 to an explicit algebraic representation of the convex hull of feasible solutions at level-n. While exponential in both the number of variables and constraints, level-n was shown in the previous chapter to serve as a useful tool for promoting valid inequalities and facets via a projection operation onto the original variable space. In this chapter, we once again invoke the convex hull representation at level-n, this time to provide a direct linkage between discrete sets and their polyhedral relaxations. Specifically, we study conditions under which a binary variable realizing a value of either 0 or 1 in an optimal solution to the linear programming relaxation of a mixed 0–1 linear program will persist in maintaining that same value in some discrete optimum.


Dual Solution Continuous Relaxation Complementary Slackness Optimal Dual Solution Persistency Property 
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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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