ContinuousOptimizationContext Constructor

public ContinuousOptimizationContext(
	Func<DoubleMatrix, double> objectiveFunction,
	DoubleMatrix initialArgument,
	double meanSmoothingCoefficient,
	double standardDeviationSmoothingCoefficient,
	int standardDeviationSmoothingExponent,
	double initialStandardDeviation,
	double terminationTolerance,
	OptimizationGoal optimizationGoal,
	int minimumNumberOfIterations,
	int maximumNumberOfIterations
)

Public Sub New ( 
	objectiveFunction As Func(Of DoubleMatrix, Double),
	initialArgument As DoubleMatrix,
	meanSmoothingCoefficient As Double,
	standardDeviationSmoothingCoefficient As Double,
	standardDeviationSmoothingExponent As Integer,
	initialStandardDeviation As Double,
	terminationTolerance As Double,
	optimizationGoal As OptimizationGoal,
	minimumNumberOfIterations As Integer,
	maximumNumberOfIterations As Integer
)

public:
ContinuousOptimizationContext(
	Func<DoubleMatrix^, double>^ objectiveFunction, 
	DoubleMatrix^ initialArgument, 
	double meanSmoothingCoefficient, 
	double standardDeviationSmoothingCoefficient, 
	int standardDeviationSmoothingExponent, 
	double initialStandardDeviation, 
	double terminationTolerance, 
	OptimizationGoal optimizationGoal, 
	int minimumNumberOfIterations, 
	int maximumNumberOfIterations
)

new : 
        objectiveFunction : Func<DoubleMatrix, float> * 
        initialArgument : DoubleMatrix * 
        meanSmoothingCoefficient : float * 
        standardDeviationSmoothingCoefficient : float * 
        standardDeviationSmoothingExponent : int * 
        initialStandardDeviation : float * 
        terminationTolerance : float * 
        optimizationGoal : OptimizationGoal * 
        minimumNumberOfIterations : int * 
        maximumNumberOfIterations : int -> ContinuousOptimizationContext

Parameters

objectiveFunction  Func<DoubleMatrix, Double>

The function to be optimized.

initialArgument  DoubleMatrix

The means of the Cross-Entropy parameter initially exploited to sample arguments of the function while searching for the optimal one.

meanSmoothingCoefficient  Double

A coefficient to define the smoothing scheme for the means of the Cross-Entropy parameters exploited by this context.

standardDeviationSmoothingCoefficient  Double

The coefficient that defines the base smoothing scheme for the standard deviations of the Cross-Entropy parameters exploited by this context.

standardDeviationSmoothingExponent  Int32

The exponent that defines the dynamic smoothing scheme for the standard deviations of the Cross-Entropy parameters exploited by this context.

initialStandardDeviation  Double

The value assigned to each standard deviation in the initial Cross-Entropy parameter exploited by this context.

terminationTolerance  Double

The minimal value which, if greater than all the standard deviations of a Cross-Entropy parameter, signals that the optimization must be considered as converged at intermediate iterations.

optimizationGoal  OptimizationGoal

A constant to specify if the function must be minimized or maximized.

minimumNumberOfIterations  Int32

The minimum number of iterations required by this context.

maximumNumberOfIterations  Int32

The maximum number of iterations allowed by this context.

It is assumed that the objectiveFunction will accept row vectors as valid representations of an argument. As a consequence, initialArgument is expected to be a row vector.

As discussed by Rubinstein and Kroese, Remark 5.2, p. 189^[1], typical values for meanSmoothingCoefficient are between .7 and 1 (excluded), while standardDeviationSmoothingCoefficient should be between .8 and 1 (excluded), with standardDeviationSmoothingExponent between 5 and 10.

Also, it is expected that initialStandardDeviation is a big enough number, such as 100.0. In this way, during the first execution of the sampling step, each argument will have a good likelihood of being drawn.

Reference