Handelman’s hierarchy for the maximum stable set problem

  title={Handelman’s hierarchy for the maximum stable set problem},
  author={Monique Laurent and Zhao Sun},
  journal={Journal of Global Optimization},
  • M. Laurent, Z. Sun
  • Published 31 May 2013
  • Mathematics
  • Journal of Global Optimization
The maximum stable set problem is a well-known NP-hard problem in combinatorial optimization, which can be formulated as the maximization of a quadratic square-free polynomial over the (Boolean) hypercube. We investigate a hierarchy of linear programming relaxations for this problem, based on a result of Handelman showing that a positive polynomial over a polytope with non-empty interior can be represented as conic combination of products of the linear constraints defining the polytope. We… 
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