Lower Bound

Definition

The LowerBound quadratic constraint ensures that a scalar value l remains above a given limit σ.

Requirements

To use the LowerBound constraint the following variables must be defined in the solver:

• l : Scalar variable being constrained.
• λ : Scalar variable used as dummy value.

Suggestions

If vertices and segment lengths are both added as variables in the solver, the CoherentLength constraint is generally used to enforce the equality between the length variable and the distance of two points. In this case, it is recommended to use the LowerBound constraint on the lengths to assure the positivity of the variables. Indeed, the CoherentLength assures the equality between the squared values.

Constraint Formulation

The formulation of the LowerBound quadratic constraint reads :

Hence, the local problem can be expressed as follow:

, , ,