h1. 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,
{mathdisplay}
\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}
{mathdisplay}

CPLEX checks for violated user cuts at the highlighted stage in the diagram below.
{gliffy:name=userCutCplex|align=left|size=L|version=1}