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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: 7.3
Syntax
public class LagrangianFunction : DoubleParameterizedFunctional

The LagrangianFunction type exposes the following members.

Constructors
  NameDescription
Public methodLagrangianFunction
Constructs a LagrangianFunction for the given objective function and constraints.
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Properties
  NameDescription
Public propertyCentralDifferenceDelta
Gets and sets the delta used in the centeral difference method for approximating the gradient with respect to the parameters.
(Inherited from DoubleParameterizedFunctional.)
Public propertyXDimension
Gets and sets the dimension of the domain of the functional.
(Inherited from DoubleParameterizedFunctional.)
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Methods
  NameDescription
Public methodClone
Returns a deep copy of the base. Deriving classes must override this method.
(Inherited from DoubleParameterizedFunctional.)
Public methodEvaluate(DoubleVector, DoubleVector)
Evaluates the parameterized function for the given parameter values at the given point.
(Overrides DoubleParameterizedFunctionalEvaluate(DoubleVector, DoubleVector).)
Public methodEvaluate(DoubleVector, DoubleMatrix, DoubleVector)
Evaluates the parameterized function for the given parameter values at the given set of points.
(Inherited from DoubleParameterizedFunctional.)
Public methodGradientWithRespectToParams
Method for calculating the gradient with respect to the parameters while keeping x fixed at the specified value.
(Inherited from DoubleParameterizedFunctional.)
Public methodGradientWithRespectToX(DoubleVector, DoubleVector)
Evaluates the gradient with respect to x at the given point.
Public methodGradientWithRespectToX(DoubleVector, DoubleVector, DoubleVector)
Evaluates the gradient with respect to x at the given point.
Public methodHessianWithRespectToX
Calcuates the Hessian matrix with respect to x.
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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)]

See Also