The objective function. The bounds on the variables. The set of linear constraint functions The bounds on the linear constraint functions The set of non-linear constraint functions The bounds on the non-linear constraint functions The point at which the minimum occurs This states that the simple bounds are satisfied at the minimum. 1 This states that the linear constraints are satisfied at the minimum. 1 This states that the non-linear constraints are satisfied at the minimum. 1 This states that for all values x which satisfy all three sets of constraints, the value of objective evaluated at x is greater than or equal to the minimum. 1 1 1