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LagrangianFunction Class

Class LagrangianFunction represents the Lagrangian function associated with a nonlinear programming problem.
Inheritance Hierarchy
SystemObject
  CenterSpace.NMath.CoreDoubleParameterizedFunctional
    CenterSpace.NMath.CoreLagrangianFunction

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