Column generation is a linear programming method that, when combined with appropriate integer programming techniques, has been successfully used for solving huge integer programs. The method alternates between a restricted master problem and a column generation subproblem. The latter step is founded on dual information from the former one; often an optimal dual solution to the linear programming relaxation of the restricted master problem is used.

We consider a zero–one linear programming problem that is approached by column generation and present a generic sufficient optimality condition for the restricted master problem to contain the columns required to find an integer optimal solution to the complete problem. The condition is based on dual information, but not necessarily on an optimal dual solution. It is however most natural to apply the condition in a situation when an optimal or near-optimal dual solution is at hand.

We relate our result to a few special cases from the literature, and make some suggestions regarding possible exploitation of the optimality condition in the construction of column generation methods for integer programs.

列生成是一种线性编程方法，当与适当的整数编程技术结合使用时，已成功用于解决大型整数程序。该方法在受限的主问题和列生成子问题之间交替。后面的步骤基于前者的双重信息。通常使用对偶主问题的线性规划松弛的最佳对偶解。

我们考虑列生成要解决的零线性规划问题，并为受限主问题提供一个通用的充分最优条件，以包含找到完整问题的整数最优解所需的列。条件基于双重信息，但不一定基于最佳双重解决方案。但是，最理想的情况是在最佳或接近最佳对偶解出现的情况下应用该条件。

我们将我们的结果与文献中的一些特殊情况联系起来，并对在整数程序的列生成方法的构造中可能利用最佳条件提出一些建议。