LagrangianFunction Class

Class LagrangianFunction represents the Lagrangian function associated with a nonlinear programming problem.

Inheritance Hierarchy

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4

Syntax

public class LagrangianFunction : DoubleParameterizedFunctional

Public Class LagrangianFunction
	Inherits DoubleParameterizedFunctional

public ref class LagrangianFunction : public DoubleParameterizedFunctional

type LagrangianFunction = 
    class
        inherit DoubleParameterizedFunctional
    end

The LagrangianFunction type exposes the following members.

Constructors

	Name	Description
	LagrangianFunction	Constructs a LagrangianFunction for the given objective function and constraints.

Properties

	Name	Description
	CentralDifferenceDelta	Gets and sets the delta used in the centeral difference method for approximating the gradient with respect to the parameters. (Inherited from DoubleParameterizedFunctional)
	XDimension	Gets and sets the dimension of the domain of the functional. (Inherited from DoubleParameterizedFunctional)

Methods

	Name	Description
	Clone	Returns a deep copy of the base. Deriving classes must override this method. (Inherited from DoubleParameterizedFunctional)
	Evaluate(DoubleVector, DoubleVector)	Evaluates the parameterized function for the given parameter values at the given point. (Overrides DoubleParameterizedFunctionalEvaluate(DoubleVector, DoubleVector))
	Evaluate(DoubleVector, DoubleMatrix, DoubleVector)	Evaluates the parameterized function for the given parameter values at the given set of points. (Inherited from DoubleParameterizedFunctional)
	GradientWithRespectToParams	Method for calculating the gradient with respect to the parameters while keeping x fixed at the specified value. (Inherited from DoubleParameterizedFunctional)
	GradientWithRespectToX(DoubleVector, DoubleVector)	Evaluates the gradient with respect to x at the given point.
	GradientWithRespectToX(DoubleVector, DoubleVector, DoubleVector)	Evaluates the gradient with respect to x at the given point.
	HessianWithRespectToX	Calcuates the Hessian matrix with respect to x.

Remarks

The Lagrangian function associated with the nonlinear programming problem

minimize f(x) subject to
ci(x) == 0, for i in E,
ci(x) >= 0 for i in I,

is defined as

L(x, lambda) = f(x) - sum[lambdai*ci(x)]