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  • Extreme.Mathematics.Optimization
    • BoundedQuasiNewtonOptimizer Class
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    • OneDimensionalOptimizer Class
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    • PowellOptimizer Class
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  • GoldenSectionOptimizer Class
    • GoldenSectionOptimizer Constructors
    • GoldenSectionOptimizer Properties
    • Methods

GoldenSectionOptimizer Class

Extreme Optimization Numerical Libraries for .NET Professional
Implements a one-dimensional optimizer that decreases the search interval by the Golden Ratio.
Inheritance Hierarchy

SystemObject
  Extreme.Mathematics.AlgorithmsManagedIterativeAlgorithmDouble, Double, SolutionReportDouble, Double
    Extreme.Mathematics.AlgorithmsManagedIterativeAlgorithmDouble
      Extreme.Mathematics.OptimizationOneDimensionalOptimizer
        Extreme.Mathematics.OptimizationGoldenSectionOptimizer

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 class GoldenSectionOptimizer : OneDimensionalOptimizer
Public Class GoldenSectionOptimizer
	Inherits OneDimensionalOptimizer
public ref class GoldenSectionOptimizer : public OneDimensionalOptimizer
type GoldenSectionOptimizer =  
    class
        inherit OneDimensionalOptimizer
    end

The GoldenSectionOptimizer type exposes the following members.

Constructors

  NameDescription
Public methodGoldenSectionOptimizer
Constructs a new GoldenSectionOptimizer object.
Public methodGoldenSectionOptimizer(ExtremumType)
Constructs a new GoldenSectionOptimizer object.
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Properties

  NameDescription
Public propertyConvergenceTests
Gets the collection of convergence tests for the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyDerivativeOfObjectiveFunction
Gets or sets the derivative of the objective function.
(Inherited from OneDimensionalOptimizer.)
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.)
Protected propertyEvaluationsRemaining
Gets the number of evaluations still available.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyExtremum
Gets the approximation to the extremum after the algorithm has run.
(Inherited from OneDimensionalOptimizer.)
Public propertyExtremumType
Gets or sets the type of extremum.
(Inherited from OneDimensionalOptimizer.)
Public propertyHasSharedDegreeOfParallelism
Indicates whether the degree of parallelism is a property that is shared across instances.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyIsBracketValid
Gets whether the algorithm's current bracket is valid.
(Inherited from OneDimensionalOptimizer.)
Public propertyIterationsNeeded
Gets the number of iterations needed by the algorithm to reach the desired accuracy.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected propertyIterationsRemaining
Gets the number of iterations remaining.
(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 OneDimensionalOptimizer.)
Public propertyObjectiveFunctionWithDerivative
Gets or sets a function that computes the value of the objective function and its derivative.
(Inherited from OneDimensionalOptimizer.)
Public propertyParallelOptions
Gets or sets the configuration for the parallel behavior of the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertyResult
Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertySolutionReport
Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public propertySolutionTest
Gets the convergence test that uses the solution of the optimization.
(Inherited from OneDimensionalOptimizer.)
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 OneDimensionalOptimizer.)
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 the value of the objective function at the approximation to the extremum after the algorithm has run.
(Inherited from OneDimensionalOptimizer.)
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Methods

  NameDescription
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodEvaluate
Evaluates the objective function.
(Inherited from OneDimensionalOptimizer.)
Protected methodEvaluateDerivative
Evaluates the derivative of the objective function.
(Inherited from OneDimensionalOptimizer.)
Protected methodEvaluateWithDerivative
Evaluates the objective function and its derivative.
(Inherited from OneDimensionalOptimizer.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodFindBracket
Finds an interval that brackets the extremum, starting from the interval [0,1].
(Inherited from OneDimensionalOptimizer.)
Public methodFindBracket(Double)
Finds an interval that brackets the extremum, starting from an interval of unit width centered around the specified point.
(Inherited from OneDimensionalOptimizer.)
Public methodFindBracket(Double, Double)
Finds an interval that brackets the extremum, starting from an interval with the specified bounds.
(Inherited from OneDimensionalOptimizer.)
Public methodFindBracket(Double, Double, Double)
Finds an interval that brackets the extremum, starting from an interval with the specified bounds and interior point.
(Inherited from OneDimensionalOptimizer.)
Public methodFindExtremum
Searches for an extremum.
(Inherited from OneDimensionalOptimizer.)
Public methodFindMaximum(FuncDouble, Double, Double)
Computes a maximum of the specified function.
(Inherited from OneDimensionalOptimizer.)
Public methodFindMaximum(FuncDouble, Double, Double, Double)
Computes a maximum of the specified function.
(Inherited from OneDimensionalOptimizer.)
Public methodFindMinimum(FuncDouble, Double, Double)
Computes a minimum of the specified function.
(Inherited from OneDimensionalOptimizer.)
Public methodFindMinimum(FuncDouble, Double, Double, Double)
Computes a minimum of the specified function.
(Inherited from OneDimensionalOptimizer.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodIncrementEvaluations
Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodIncrementEvaluations(Int32)
Increments the number of evaluations by the specified amount.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodIterate
Performs one iteration of the algorithm.
(Overrides ManagedIterativeAlgorithmT, TError, TReportIterate.)
Protected methodIterated
Performs tasks after the iteration is completed, but before the status of the algorithm is finalized.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Protected methodOnConvergence
Performs any tasks after the main algorithm has converged.
(Inherited from OneDimensionalOptimizer.)
Protected methodOnFailure
Performs any tasks after the main algorithm has failed to converge.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodOnInit
Performs initialization before the first iteration.
(Overrides OneDimensionalOptimizerOnInit.)
Protected methodReportFailure
Records the results of an algorithm in case it fails.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodReportResult
Records the results of an algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodReportSuccess
Records the results of a algorithm that converged successfully.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodResetEvaluations
Resets the number of evaluations to zero.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodRestart
Prepares the algorithm to be run again with possibly different inputs.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodRun
Runs the algorithm.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodRun(ParallelOptions)
Runs the algorithm using the specified parallelization options.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodSetResult
Sets the results of an algorithm's execution.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodTestConvergence
Checks whether the algorithm has converged.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodThreadSafeIncrementEvaluations
Increments the number of evaluations by one.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodThreadSafeIncrementEvaluations(Int32)
Increments the number of evaluations by the specified amount.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Protected methodThrowConvergenceException
Interprets the AlgorithmStatus and throws the appropriate exception.
(Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

Use the GoldenSectionOptimizer to find the minimum or a maximum of a function.

The ObjectiveFunction property must be set to a function of one variable that evaluates the objective function. The ExtremumType property specifies whether a maximum or a minimum of the objective function is requested.

The algorithm itself runs in two phases. In the bracketing phase, a search is made for an interval that is known to contain an extremum. This step is performed automatically when the algorithm is run. You can run it manually by calling one of the FindBracket(Double) methods. You can check the validity of a bracketing interval by inspecting the IsBracketValid property.

Once a bracketing interval has been found, the location phase begins. The exact location of the extremum is found by successively narrowing the bracketing interval. This phase always converges for continuous functions. The FindExtremum method performs the location phase, and returns the best approximation to the extremum. Alternatively, one of the FindMaximum(FuncDouble, Double, Double, Double) or FindMinimum(FuncDouble, Double, Double, Double) methods can be used. This has the advantage that the objective function as well as an initial guess can be supplied with the method call.

The Extremum property returns the best approximation to the extremum. The EstimatedError property returns the uncertainty of 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 a bracketing interval could not be found.

Convergence is tested using a simple convergence test based on the uncertainty in the location of the approximate extremum. The SolutionTest property returns a SimpleConvergenceTestT object that allows you to specify the desired Tolerance and specific ConvergenceCriterion.

See Also

Reference

Extreme.Mathematics.Optimization Namespace
Extreme.Mathematics.OptimizationBrentOptimizer
Extreme.Mathematics.OptimizationBrentDerivativeOptimizer

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