﻿LagrangianFunction Class

# 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
LagrangianFunction
Constructs a LagrangianFunction for the given objective function and constraints.
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Properties
NameDescription
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.)
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Methods
NameDescription
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.)
Method for calculating the gradient with respect to the parameters while keeping x fixed at the specified value.
(Inherited from DoubleParameterizedFunctional.)
Evaluates the gradient with respect to x at the given point.
Evaluates the gradient with respect to x at the given point.
HessianWithRespectToX
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)]