A new warmstarting strategy for the primal-dual column generation method

Jacek Gondzio, Pablo Gonzalez-Brevis

Research output: Contribution to journalArticlepeer-review


This paper presents a new warmstarting technique in the context of a primal-dual column generation method applied to solve a particular class of combinatorial optimization problems. The technique relies on calculating an initial point and on solving auxiliary linear optimization problems to determine the step direction needed to fully restore primal and dual feasibilities after new columns arrive. Conditions on the maximum size of the cuts and on a suitable initial point are discussed. Additionally, the strategy ensures that the duality gap of the warmstart is bounded by the old duality gap multiplied with a (small) constant, which depends on the relation between the old and modified problems. Computational experiments demonstrate the gains achieved when compared to a coldstart approach.
Original languageEnglish
Pages (from-to)113-146
JournalMathematical programming
Issue number1-2
Early online date22 May 2014
Publication statusPublished - 31 Aug 2015


  • Interior point methods
  • Warmstarting
  • Column generation
  • Linear programming
  • Cutting stock problem
  • Vehicle routing problem with time windows


Dive into the research topics of 'A new warmstarting strategy for the primal-dual column generation method'. Together they form a unique fingerprint.

Cite this