The piecewise linear optimization polytope: New inequalities and intersection with semi-continuous constraints

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Abstract

We give new facets and valid inequalities for the separable piecewise linear optimization (SPLO) knapsack polytope. We also extend the inequalities to the case in which some of the variables are semi-continuous. Finally, we give computational results that demonstrate their efficiency in solving difficult instances of SPLO and SPLO with semi-continuous constraints.

Original languageEnglish
Pages (from-to)217-255
Number of pages39
JournalMathematical Programming
Volume141
Issue number1-2
DOIs
StatePublished - Oct 2013

Keywords

  • Branch-and-cut
  • Knapsack problem
  • Mixed-integer programming
  • Piecewise linear optimization
  • Polyhedral method
  • Semi-continuous variables
  • Special ordered set

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