ModifiedLevenbergMarquardtMinimizerMinimize(DoubleMultiVariableFunction, DoubleVector, Double) Method

Minimizes the L2 norm of the given function near the given starting point.

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

Syntax

public DoubleVector Minimize(
	DoubleMultiVariableFunction f,
	DoubleVector x0,
	double mu0
)

Public Function Minimize ( 
	f As DoubleMultiVariableFunction,
	x0 As DoubleVector,
	mu0 As Double
) As DoubleVector

public:
DoubleVector^ Minimize(
	DoubleMultiVariableFunction^ f, 
	DoubleVector^ x0, 
	double mu0
)

member Minimize : 
        f : DoubleMultiVariableFunction * 
        x0 : DoubleVector * 
        mu0 : float -> DoubleVector

Parameters

f DoubleMultiVariableFunction: Function whose norm is to be minimized.
x0 DoubleVector: Starting point for the iteration.
mu0 Double: Initial value for mu in the Modified Levenberg Marquardt algorithm. The default value is 1e-5.

Return Value

DoubleVector
The solution.

Remarks

The value mu is used in the LM algorithm as follows: At the kth iteration with current solution = xk, denote: Jk == J(xk), the Jacobian value at xk, Fk = F(xk), the value of the objective function at xk, muk = the value of mu at iteration k. Then the Levenberg Marquardt step dk is defined as the solution to the linear system: (Jk'*Jk - lambdak*I)dk = -Jk*Fk, lambak = muk*||Fk||.

Reference

ModifiedLevenbergMarquardtMinimizer Class

Minimize Overload

CenterSpace.NMath.Core Namespace