Constraint

Formulation

The local formulation of the constraint's quadratic equation reads :

where :

• H_i,red : Symmetric matrix.
• b_i,red : Column vector.
• c_i : Scalar value.

Custom Constraint Type

Custom Quadratic Constraint Type

Create a public class which inherits from the IQuadraticConstraintType interface and declare the three properties required to implement the interface. These three properties correspond to the local symmetric matrix H_i,red, the column vector b_i and the scalar coefficient c_i necessary to define a linear constraint from vector x_red.

public class CostumQuadraticConstraintName : IQuadraticConstraintType
{
  /// <inheritdoc/>
  public DictionaryOfKeys LocalHi { get; }

  /// <inheritdoc/>
  public Dictionary<int, double> LocalKi { get; }

  /// <inheritdoc/>
  public double Si { get; }

  ...

}

Then, in the class constructor, instanciate and initialise the values of the properties. The parameters of the constructor should provide the information needed to fill in H_i,red, b_i and c_i.

  public CostumQuadraticConstraintName()
  {
    ...
  }

Cusoum Linearised Constraint Type

Create a public class which inherits from the ILinearisedConstraintType interface and declare the three properties required to implement the interface. These three properties correspond to the local symmetric matrix H_i,red, the column vector b_i and the scalar coefficient c_i necessary to define a linear constraint from vector x_red.

public class CostumLinearisedConstraintName : ILinearisedConstraintType
{
  /// <inheritdoc/>
  public DictionaryOfKeys LocalHi { get; }

  /// <inheritdoc/>
  public Dictionary<int, double> LocalKi { get; }

  /// <inheritdoc/>
  public double Si { get; }

  ...

}

Then, leave the class constructor empty.

  public CostumLinearisedConstraintName()
  {
    ...
  }

Finally, declare an update method for the properties of the costum linearised constraint type. The parameter xReduced of the method contains the updated value of the variables'components. The order of the components in xReduced follows the order in which the variables where are added in the ensuing LinearisedConstraint. This method will be called at each iteration during the solving process with the updated values of xReduced.

  void UpdateLocal(double[] xReduced);
  {
    /* Update the values of the properties using xReduced */
  }

Implemented Constraint Types

Implemented Quadratic Constraints Types

The following energies can be found in BRIDGES.Solvers.GuidedProjection.QuadraticConstraintTypes namespace.

Coherent Length

Constraint enforcing a scalar variable l to match with the distance between two point variables, p_i and p_j. For more information, see the dedicated page.

Lower Bound

Constraint enforcing a value variable l to be higher than a lower bound σ using a dummy value variable λ. For more information, see the dedicated page.

Upper Bound

Constraint enforcing a value variable l to be lower than an upper bound σ using a dummy value variable λ. For more information, see the dedicated page.

Vector Length

Constraint enforcing a vector variable v to have a given length l (computed with euclidean norm). For more information, see the dedicated page.

Implemented Linearised Constraint Types

The following energies can be found in BRIDGES.Solvers.GuidedProjection.LinearisedConstraintTypes namespace.

No linearised constraints are defined yet