Methods for generating bounds on the optimal value of a MILP are essential to the development of effective solution procedures. Traditionally, bounding methods based on decomposition, such as Dantzig-Wolfe decomposition and Lagrangian relaxation, have been treated as distinct both from each other and from polyhedral methods that utilize dynamic cut generation for bound improvement. It is possible, however, to view these methods from a common theoretical perspective and to integrate them in order to capitalize on their individual strengths. In this talk, we introduce both a theoretical framework that takes this perspective and a software framework that implements the resulting methodology, allowing for explicit experimentation with the tradeoffs among various decomposition approaches.
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