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    • BoundedQuasiNewtonOptimizer Class
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  • NelderMeadOptimizer Class
    • NelderMeadOptimizer Constructor
    • Properties
    • NelderMeadOptimizer Methods

NelderMeadOptimizer Class

Extreme Optimization Numerical Libraries for .NET Professional
Implements the Nelder-Mead simplex algorithm for multi-dimensional optimization.
Inheritance Hierarchy

SystemObject
  Extreme.Mathematics.AlgorithmsManagedIterativeAlgorithmVectorDouble, Double, OptimizationSolutionReport
    Extreme.Mathematics.OptimizationMultidimensionalOptimizer
      Extreme.Mathematics.OptimizationNelderMeadOptimizer

Namespace:  Extreme.Mathematics.Optimization
Assembly:  Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
Syntax

C#
VB
C++
F#
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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.

Constructors

  NameDescription
Public methodNelderMeadOptimizer
Constructs a new NelderMeadOptimizer object.
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Properties

  NameDescription
Public propertyContractionFactor
Gets or sets the factor used in a contraction step of the algorithm.
Public propertyConvergenceTests
Gets the collection of convergence tests for the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyDimensions
Gets or sets the number of dimensions of the optimization problem.
(Inherited from MultidimensionalOptimizer.)
Public propertyEstimatedError
Gets a value indicating the size of the absolute error of the result.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyEvaluationsNeeded
Gets the number of evaluations needed to execute the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyExpansionFactor
Gets or sets the factor by which the simplex is extended in the direction of the current best point.
Public propertyExtremum
Gets or sets the current best approximation to the extremum.
(Inherited from MultidimensionalOptimizer.)
Public propertyExtremumType
Gets or sets the type of extremum.
(Inherited from MultidimensionalOptimizer.)
Public propertyFastGradientFunction
Gets or sets the function that computes the gradient of the objective funciton.
(Inherited from MultidimensionalOptimizer.)
Public propertyGradientEvaluationsNeeded
Gets the number of evaluations of the gradient of the objective function.
(Inherited from MultidimensionalOptimizer.)
Public propertyGradientFunction
Gets or sets the function that computes the gradient of the objective funciton.
(Inherited from MultidimensionalOptimizer.)
Public propertyGradientTest
Gets the VectorConvergenceTestT that uses the gradient of the objective function.
(Inherited from MultidimensionalOptimizer.)
Public propertyGradientVector
Gets or sets the current value of the gradient.
(Inherited from MultidimensionalOptimizer.)
Public propertyHasSharedDegreeOfParallelism
Indicates whether the degree of parallelism is a property that is shared across instances.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyInitialGuess
Gets or sets the initial value for the iteration.
(Inherited from MultidimensionalOptimizer.)
Public propertyIterationsNeeded
Gets the number of iterations needed by the algorithm to reach the desired accuracy.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyMaxDegreeOfParallelism
Gets or sets the maximum degree of parallelism enabled by this instance.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyMaxEvaluations
Gets or sets the maximum number of evaluations during the calculation.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyMaxIterations
Gets or sets the maximum number of iterations to use when approximating the roots of the target function.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyMinIterations
Gets or sets the minimum iterations that have to be performed.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyObjectiveFunction
Gets or sets the objective function.
(Inherited from MultidimensionalOptimizer.)
Public propertyObjectiveFunctionWithGradient
Gets or sets a function that evaluates the value and gradient of the objective function.
(Inherited from MultidimensionalOptimizer.)
Public propertyParallelOptions
Gets or sets the configuration for the parallel behavior of the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyReflectionFactor
Gets or sets the factor by which the simplex is reflected away from the worst point.
Public propertyResult
Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyScale
Gets or sets the size of the initial simplex.
Public propertyShrinkageFactor
Gets or sets the factor by which the simplex is shrunk towards the best point.
Public propertySolutionReport
Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertySolutionTest
Gets the VectorConvergenceTestT that uses the approximate solution.
(Inherited from MultidimensionalOptimizer.)
Public propertyStatus
Gets the AlgorithmStatus following an execution of the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertySymbolicObjectiveFunction
Gets or sets the objective function.
(Inherited from MultidimensionalOptimizer.)
Public propertyThrowExceptionOnFailure
Gets or sets a value indicating whether to throw an exception when the algorithm fails to converge.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyValueAtExtremum
Gets or sets the current value of the objective function.
(Inherited from MultidimensionalOptimizer.)
Public propertyValueTest
Gets the SimpleConvergenceTestT that uses the value of the target functions.
(Inherited from MultidimensionalOptimizer.)
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Methods

  NameDescription
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodFindExtremum
Searches for an extremum.
(Inherited from MultidimensionalOptimizer.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

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.

See Also

Reference

Extreme.Mathematics.Optimization Namespace

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