Column generation

The graph of a strictly concave quadratic function is shown in blue, with its unique maximum shown as a red dot. Below the graph appears the contours of the function: The level sets are nested ellipses.

Column generation or delayed column generation is an efficient algorithm for solving larger linear programs.

The overarching idea is that many linear programs are too large to consider all the variables explicitly. Since most of the variables will be non-basic and assume a value of zero in the optimal solution, only a subset of variables need to be considered in theory when solving the problem. Column generation leverages this idea to generate only the variables which have the potential to improve the objective function—that is, to find variables with negative reduced cost (assuming without loss of generality that the problem is a minimization problem).

单词	Column generation
释义	Column generation 英语百科 Column generation Column generation or delayed column generation is an efficient algorithm for solving larger linear programs. The overarching idea is that many linear programs are too large to consider all the variables explicitly. Since most of the variables will be non-basic and assume a value of zero in the optimal solution, only a subset of variables need to be considered in theory when solving the problem. Column generation leverages this idea to generate only the variables which have the potential to improve the objective function—that is, to find variables with negative reduced cost (assuming without loss of generality that the problem is a minimization problem).
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