| Background | Last, we formulate our optimization problem as an Integer Linear Program (ILP). |
| Background | ILP is an optimization problem where a linear objective function over a set of integer variables is maximized under a set of linear constraints. |
| Learning Typed Entailment Graphs | Section 4.2 gives an ILP formulation for the optimization problem . |
| Learning Typed Entailment Graphs | The edges returned by the solver provide an optimal (not approximate) solution to the optimization problem . |
| Model Inference | The Lagrangian relaxation of this optimization problem is L(a, b, C(a), (:00), u) = |
| Model Inference | We can form a dual problem that is an upper bound on the original optimization problem by swapping the order of min and max. |
| Model Inference | Hence, it is also a solution to our original optimization problem : Equation 3. |