Implements the NelderMead simplex algorithm for multidimensional optimization.
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
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.
Top
 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  (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  (Inherited from MultidimensionalOptimizer.) 
 Status  (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  (Inherited from MultidimensionalOptimizer.) 
Top
Top
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 NelderMead method, and it's
Enabled property is set to
before the algorithm is executed.
Reference