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User Cuts in CPLEX
User cuts are, at a high level, valid inequalities for an integer program that strengthen the formulation, but are not required for correctness of the formulation. For example, in the 0-1 knapsack problem,
\[ \begin{aligned} &\max&\sum_{i=1}^n v_i x_i\\ &\text{subject to}& \sum_{i=1}^n w_i x_i &\leq b\\ &&x_i & \in \{0,1\}&i&=1,\ldots,n \end{aligned} \]CPLEX checks for violated user cuts at the highlighted stage in the diagram below.