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Preprint 08-2004

Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)

Selected Topics in Column Generation
primary: 90C10 Integer programming
secondary: 90-02 Research exposition
90C05 Linear programming
90C06 Large-scale problems
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
49M27 Decomposition methods
65K05 Mathematical programming algorithms
Linear Programming, Integer Programming, Column Generation, Dantzig-Wolfe decomposition, Lagrangian Relaxation, Branch-and-Bound
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.
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