Optimizationfminunconst_newton Method

ILNumerics Ultimate VS Documentation

ILNumerics - Technical Application Development

Find minimizer of a medum-scale unconstrained multivariable nonlinear optimization problem using a classical newton method with explicit hessian evaluation

[ILNumerics Optimization Toolbox]

Namespace: ILNumerics.Toolboxes
Assembly: ILNumerics.Toolboxes.Optimization (in ILNumerics.Toolboxes.Optimization.dll) Version: 5.5.0.0 (5.5.7503.3146)

Syntax

Copy

public static RetArray<double> fminunconst_newton(
	OptimizationObjectiveFunction<double> objfunc,
	InArray<double> x0,
	OptimizationDerivativeFunction<double> hessianfunc = null,
	int maxIter = 500,
	OptimizationDerivativeFunction<double> gradientFunc = null,
	OutArray<double> iterations = null,
	OutArray<double> gradientNorm = null,
	OutArray<int> iterationCount = null,
	Nullable<double> tol = null,
	Nullable<double> tolX = null
)

Public Shared Function fminunconst_newton ( 
	objfunc As OptimizationObjectiveFunction(Of Double),
	x0 As InArray(Of Double),
	Optional hessianfunc As OptimizationDerivativeFunction(Of Double) = Nothing,
	Optional maxIter As Integer = 500,
	Optional gradientFunc As OptimizationDerivativeFunction(Of Double) = Nothing,
	Optional iterations As OutArray(Of Double) = Nothing,
	Optional gradientNorm As OutArray(Of Double) = Nothing,
	Optional iterationCount As OutArray(Of Integer) = Nothing,
	Optional tol As Nullable(Of Double) = Nothing,
	Optional tolX As Nullable(Of Double) = Nothing
) As RetArray(Of Double)

Dim objfunc As OptimizationObjectiveFunction(Of Double)
Dim x0 As InArray(Of Double)
Dim hessianfunc As OptimizationDerivativeFunction(Of Double)
Dim maxIter As Integer
Dim gradientFunc As OptimizationDerivativeFunction(Of Double)
Dim iterations As OutArray(Of Double)
Dim gradientNorm As OutArray(Of Double)
Dim iterationCount As OutArray(Of Integer)
Dim tol As Nullable(Of Double)
Dim tolX As Nullable(Of Double)
Dim returnValue As RetArray(Of Double)

returnValue = Optimization.fminunconst_newton(objfunc, 
	x0, hessianfunc, maxIter, gradientFunc, 
	iterations, gradientNorm, iterationCount, 
	tol, tolX)

Parameters

objfunc: Type: ILNumerics.ToolboxesOptimizationObjectiveFunctionDouble
Cost function to be minimized, defined from Rⁿ to R
x0: Type: ILNumericsInArrayDouble
Initial solution guess, lenght: (Rⁿ). Specifies the starting point for the search.
hessianfunc (Optional): Type: ILNumerics.ToolboxesOptimizationDerivativeFunctionDouble
[optional] Custom function for computing the hessian matrix of objfunc. Default: null hessian(OptimizationObjectiveFunctionDouble, InArrayDouble, InArrayDouble))
maxIter (Optional): Type: SystemInt32
[optional] Maximal number of iterations allowed. Default: 500
gradientFunc (Optional): Type: ILNumerics.ToolboxesOptimizationDerivativeFunctionDouble
[optional] Function used to compute the gradient. Default: null (finite differences via jacobian_prec)
iterations (Optional): Type: ILNumericsOutArrayDouble
[optional] Output array of intermediate positions at each iteration. Default: null (not provided)
gradientNorm (Optional): Type: ILNumericsOutArrayDouble
[optional] Output: Request the gradient norms at each iteration. Default: null (do not compute)
iterationCount (Optional): Type: ILNumericsOutArrayInt32
[Output] Number of effective iterations during the computation
tol (Optional): Type: SystemNullableDouble
[optional] Exit tolerance on the gradient. Default: DefaultTolerance (1e-8)
tolX (Optional): Type: SystemNullableDouble
[optional] Exit the iterations when the solution is not significantly changing anymore. Default: DefaultTolerance (1e-8)

Return Value

Type: RetArrayDouble
A local minimizer of func, length: n

Exceptions

Exception	Condition
ArgumentOutOfRangeException	If objfunc is not defined at x0 or if objfunc was found to be non-scalar
ArgumentNullException	If one of x0 or objfunc was null on entry

Remarks

If x0 is empty, an empty array of the same size will be returned.

This function computes the local minimum of the scalar multivariable non-linear optimization problem by explicitly evaluating the hessian matrix. If no hessian function is provided by the user, the predefined hessian(OptimizationObjectiveFunctionDouble, InArrayDouble, InArrayDouble) function evaluation will be used (finite differences). This leads to very precise results but is rather expensive for demanding problems. In order to control the hessian computation, user can provide a custom hessian function as OptimizationDerivativeFunctionT.

[ILNumerics Optimization Toolbox]

Examples

Copy

Array<double> x0 = -8 *ILMath.ones(2, 1); // initial guess for the solution 
Array<double> Mini = Optimization.fminunconst_newton(SampleFunction, x0, hessianfunc: Optimization.hessian); // minimizer of the SampleFuntion in two dimensions; 
// the hessian argument provided above corresponds to the defaul argument. 

//Sample function definition
public static RetArray<double> SampleFunction(InArray<double> A)
{
   using (Scope.Enter(A))
   {
       return 2 * x[0] * x[0] + x[0] * x[1] + 2 * x[1] * x[1] - 6 * x[0] - 6 * x[1] + 15;
   }
}

Reference

Optimization Class

ILNumerics.Toolboxes Namespace

Other Resources

http://ilnumerics.net/unconstrained-optimization.html

OptimizationAddLanguageSpecificTextSet("LST35A762A6_0?cpp=::|nu=.");fminunconst_newton Method

Parameters

Return Value

Reference

Other Resources

Optimizationfminunconst_newton Method