Inequality constraint

Terminology

• If an inequality constraint holds with equality at the optimal point, the constraint is said to be binding, as the point cannot be varied in the direction of the constraint even though doing so would improve the value of the objective function.
• If an inequality constraint holds as a strict inequality at the optimal point (that is, does not hold with equality), the constraint is said to be non-binding, as the point could be varied in the direction of the constraint, although it would not be optimal to do so. Under certain conditions, as for example in convex optimization, if a constraint is non-binding, the optimization problem would have the same solution even in the absence of that constraint.
• If a constraint is not satisfied at a given point, the point is said to be infeasible.