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Optimization Letters

, Volume 13, Issue 2, pp 235–248 | Cite as

Matrices with lexicographically-ordered rows

  • Gustavo AnguloEmail author
Original Paper
  • 37 Downloads

Abstract

The lexicographic order can be used to force a collection of decision vectors to be all different, i.e., to take on different values in some coordinates. We consider the set of fixed-size matrices with bounded integer entries and rows in lexicographic order. We present a dynamic program to optimize a linear function over this set, from which we obtain a compact extended formulation for its convex hull.

Keywords

Lexicographic order Extended formulation Dynamic programming 

Notes

Acknowledgements

The author thanks an anonymous referee whose comments and suggestions greatly helped to improve the paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringPontificia Universidad Católica de ChileSantiagoChile

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