The binding threshold for constraints.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public double BindingThreshold { get; set; }
Visual Basic (Declaration)
Public Property BindingThreshold As Double
Visual C++
public:
property double BindingThreshold {
	double get ();
	void set (double value);
}

Field Value

A double scalar value specifying the binding threshold for constraints.

Remarks

In the initial phase of minimization a constraint is considered binding if   \frac{g_i \left( x \right)}{max \left(
            1,\|\nabla g_i \left( x \right) \| \right)} \leq \mbox{\it BindingThreshold} \ \
            \ \ \ \ i=M_e + 1,\dots,M

Good values are between .01 and 1.0. If BindingThreshold is chosen too small then identification of the correct set of binding constraints may be delayed. Contrary, if BindingThreshold is too large, then the method will often escape to the full regularized SQP method, using individual slack variables for any active constraint, which is quite costly. For well scaled problems BindingThreshold = 1.0 is reasonable. By default, BindingThreshold is set to .5 * PenaltyBound.

Exceptions

ExceptionCondition
System..::.ArgumentException is thrown if BindingThreshold is less than or equal to 0.0

See Also