Column generation

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This pertains to solving a linear program whose columns are generated during pricing. Typically, the number of columns is astronomically large, possibly infinite. An example is when solving the randomized program, as with the Generalized Lagrange Multiplier method. In that case, column generation consists of maximizing the Lagrangian. A similar view applies to Dantzig-Wolfe decomposition. From the dual view, this is a cutting plane method since generating a column in the primal corresponds to generating a constraint in the dual.

The concept applies to any mathematical program, and the randomized program model hightlights the duality and how a completely general mathematical program can be considered with (generalized) linear programming.

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