Column Generation

Column generation is an indispensable tool in computational optimization to solve a mathematical program by iteratively adding the variables of the model. Even though the method is simple in theory there are many algorithmic choices and we discuss the most common ones. Particular emphasis in put on the dual interpretation, relating column generation to Langrangian relaxation and cutting plane algorithms, which revealed several critical issues like the need for dual variable stabilization techniques. We conclude with some advise for computer implementations.