Decomposition and Dynamic Cut Generation in Integer Programming: Theory and Algorithms

Decomposition algorithms such as Lagrangian relaxation and Dantzig-Wolfe decomposition are well-known methods that can be used to compute bounds for integer programming problems. We discuss a framework for integrating dynamic cut generation with traditional decomposition methods in order to obtain improved bounds and present a new paradigm for separation called decompose and cut. The methods we present take advantage of the fact that separation of a vector with known structure is often much easier than separation of an arbitrary one.