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Preprint 08-2004
Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)- Title
- Selected Topics in Column Generation
- Authors
- Classification
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MSC: 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 - Keywords
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Linear Programming, Integer Programming, Column Generation, Dantzig-Wolfe decomposition, Lagrangian Relaxation, Branch-and-Bound
- Abstract
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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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