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Selected Topics in Column Generation

Technische Universität Berlin, Institut für Mathematik, Sekr. MA 6-1, Straße des 17. Juni 136, D-10623 Berlin, Germany
HEC Montréal and GERAD, 3000, chemin de la Côte-Sainte-Catherine, Montréal, Québec, Canada H3T 2A7
m.luebbecke{at}math.tu-berlin.de
jacques.desrosiers{at}hec.ca

Dantzig-Wolfe decomposition and column generation, devised for linear programs, is a success story in large-scale integer programming. We outline and relate the approaches, and survey mainly recent contributions, not yet found in textbooks. We emphasize the growing understanding of the dual point of view, which has brought considerable progress to the column generation theory and practice. It stimulated careful initializations, sophisticated solution techniques for the restricted master problem and subproblem, as well as better overall performance. Thus, the dual perspective is an ever recurring concept in our "selected topics."

Subject classifications: integer programming: column generation, Dantzig-Wolfe decomposition, Lagrangian relaxation, branch-and-bound; linear programming: large scale systems.
History: Received December 2002; revision received March 2004; accepted October 2004.

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