Vector Length

Definition

The VectorLength quadratic constraint ensures that a vector variable v has a length equal to a given scalar value l.

Requirements

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

  • v : Vector variable with a finite number of coordinates.

Suggestions

No remarks.

Constraint Formulation

The formulation of the UpperBound quadratic constraint reads :

Formulation of the VectorLength constraint

which, in the case where the vector is from a three-dimensional space, develops to :

Developed formulation of the VectorLength constraint

Hence, the local problem can be expressed as follow:

Reduced vector x for the VectorLength constraint , Quadratic part of the VectorLength constraint , Linear part of the VectorLength constraint , Constant part of the VectorLength constraint

In the framework, the VectorLength constraint is not restricted to the three-dimensional case. The dimension of the space is given at initialisation of the constraint.