Optimizationfminunconst_lbfgs Method

ILNumerics Ultimate VS Documentation

ILNumerics - Technical Application Development

Find minimizer of a large-scale unconstrained multivariable nonlinear optimization problem

[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_lbfgs(
	OptimizationObjectiveFunction<double> objfunc,
	InArray<double> x0,
	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_lbfgs ( 
	objfunc As OptimizationObjectiveFunction(Of Double),
	x0 As InArray(Of Double),
	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 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_lbfgs(objfunc, 
	x0, 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.
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

This functino finds a minimizer of a large-scale unconstrained multivariable nonlinear optimization problem without evaluating the hessian matrix explicitely. For large scale problems with a large number of variables and commonly sparse derivatives, an advantageous performance scheme is achieved which allows the minimizer to be found efficiently without the need of the computation of all hessian elements explicitly.

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

[ILNumerics Optimization Toolbox]

Examples

Copy

Array<double> x0 = -8 *ILMath.ones(2, 1); // initial guess for the solution 
Array<double> Mini = Optimization.fminunconst_lbfgs(SampleFunction, x0); // minimizer of the SampleFuntion in two dimensions; 
//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("LSTAFAA3A62_0?cpp=::|nu=.");fminunconst_lbfgs Method

Parameters

Return Value

Reference

Other Resources

Optimizationfminunconst_lbfgs Method