NelderMeadOptimizer Class

public sealed class NelderMeadOptimizer : MultidimensionalOptimizer

Public NotInheritable Class NelderMeadOptimizer
	Inherits MultidimensionalOptimizer

public ref class NelderMeadOptimizer sealed : public MultidimensionalOptimizer

[<SealedAttribute>]
type NelderMeadOptimizer =  
    class
        inherit MultidimensionalOptimizer
    end

The NelderMeadOptimizer type exposes the following members.

	Name	Description
	NelderMeadOptimizer	Constructs a new NelderMeadOptimizer object.

	Name	Description
	ContractionFactor	Gets or sets the factor used in a contraction step of the algorithm.
	ConvergenceTests	Gets the collection of convergence tests for the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Dimensions	Gets or sets the number of dimensions of the optimization problem. (Inherited from MultidimensionalOptimizer.)
	EstimatedError	Gets a value indicating the size of the absolute error of the result. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	EvaluationsNeeded	Gets the number of evaluations needed to execute the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	ExpansionFactor	Gets or sets the factor by which the simplex is extended in the direction of the current best point.
	Extremum	Gets or sets the current best approximation to the extremum. (Inherited from MultidimensionalOptimizer.)
	ExtremumType	Gets or sets the type of extremum. (Inherited from MultidimensionalOptimizer.)
	FastGradientFunction	Gets or sets the function that computes the gradient of the objective funciton. (Inherited from MultidimensionalOptimizer.)
	GradientEvaluationsNeeded	Gets the number of evaluations of the gradient of the objective function. (Inherited from MultidimensionalOptimizer.)
	GradientFunction	Gets or sets the function that computes the gradient of the objective funciton. (Inherited from MultidimensionalOptimizer.)
	GradientTest	Gets the VectorConvergenceTestT that uses the gradient of the objective function. (Inherited from MultidimensionalOptimizer.)
	GradientVector	Gets or sets the current value of the gradient. (Inherited from MultidimensionalOptimizer.)
	HasSharedDegreeOfParallelism	Indicates whether the degree of parallelism is a property that is shared across instances. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	InitialGuess	Gets or sets the initial value for the iteration. (Inherited from MultidimensionalOptimizer.)
	IterationsNeeded	Gets the number of iterations needed by the algorithm to reach the desired accuracy. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MaxDegreeOfParallelism	Gets or sets the maximum degree of parallelism enabled by this instance. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MaxEvaluations	Gets or sets the maximum number of evaluations during the calculation. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MaxIterations	Gets or sets the maximum number of iterations to use when approximating the roots of the target function. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	MinIterations	Gets or sets the minimum iterations that have to be performed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	ObjectiveFunction	Gets or sets the objective function. (Inherited from MultidimensionalOptimizer.)
	ObjectiveFunctionWithGradient	Gets or sets a function that evaluates the value and gradient of the objective function. (Inherited from MultidimensionalOptimizer.)
	ParallelOptions	Gets or sets the configuration for the parallel behavior of the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	ReflectionFactor	Gets or sets the factor by which the simplex is reflected away from the worst point.
	Result	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Scale	Gets or sets the size of the initial simplex.
	ShrinkageFactor	Gets or sets the factor by which the simplex is shrunk towards the best point.
	SolutionReport	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	SolutionTest	Gets the VectorConvergenceTestT that uses the approximate solution. (Inherited from MultidimensionalOptimizer.)
	Status	Gets the AlgorithmStatus following an execution of the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	SymbolicObjectiveFunction	Gets or sets the objective function. (Inherited from MultidimensionalOptimizer.)
	ThrowExceptionOnFailure	Gets or sets a value indicating whether to throw an exception when the algorithm fails to converge. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	ValueAtExtremum	Gets or sets the current value of the objective function. (Inherited from MultidimensionalOptimizer.)
	ValueTest	Gets the SimpleConvergenceTestT that uses the value of the target functions. (Inherited from MultidimensionalOptimizer.)

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	FindExtremum	Searches for an extremum. (Inherited from MultidimensionalOptimizer.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

Use the NelderMeadOptimizer class to find an extremum of an objective function for which only the objective function is available, and the objective function itself may not be smooth. The method is often called the downhill simplex method.

The main advantage of this method is that it converges for functions where other methods would fail. This may happen, for instance, when the derivative of the objective function contains discontinuities. The major drawback is that the method converges more slowly than the other methods, and performs poorly for large problems.

The objective function must be supplied as a multivariate function delegate to the ObjectiveFunction property. The gradient of the objective function is not used.

Before the algorithm is run, you must set the InitialGuess property to a vector that contains an initial estimate for the extremum. The ExtremumType property specifies whether a minimum or a maximum of the objective function is desired.

The FindExtremum method performs the actual search for an extremum, and returns a Vector containing the best approximation. The Extremum property also returns the best approximation to the extremum. The ValueAtExtremum property returns the value of the objective function at the extremum.

The Status property is a AlgorithmStatus value that indicates the outcome of the algorithm. A value of Normal shows normal termination. A value of Divergent usually indicates that the objective function is not bounded.

The algorithm has two convergence tests. By default, the algorithm terminates when either of these is satisfied. You can deactivate either test by setting its Enabled property to . If both tests are deactivated, then the algorithm always terminates when the maximum number of iterations or function evaluations is reached.

The first test is based on the uncertainty in the location of the approximate extremum. The test succeeds if the difference between the best and worst approximation is within the tolerance. The SolutionTest property returns a VectorConvergenceTestT object that allows you to specify the desired Tolerance and specific ConvergenceCriterion. See the VectorConvergenceTestT class for details on how to further customize this test.

The second test is based on the difference in value of the objective function at the best and at the worst current approximation. The test is successful when the difference between the two is within the tolerance. Care should be taken with this test. When the tolerance is too large, the algorithm will terminate prematurely. The ValueTest property returns a SimpleConvergenceTestT object that can be used to customize the test.

A third test, based on the value of the gradient at the approximate extremum, is exposed through the GradientTest property. However, this test does not apply to the Nelder-Mead method, and it's Enabled property is set to before the algorithm is executed.

Reference