BrentOptimizer Class

public sealed class BrentOptimizer : OneDimensionalOptimizer

Public NotInheritable Class BrentOptimizer
	Inherits OneDimensionalOptimizer

public ref class BrentOptimizer sealed : public OneDimensionalOptimizer

[<SealedAttribute>]
type BrentOptimizer =  
    class
        inherit OneDimensionalOptimizer
    end

The BrentOptimizer type exposes the following members.

	Name	Description
	BrentOptimizer	Constructs a new BrentOptimizer object.
	BrentOptimizer(ExtremumType)	Constructs a new BrentOptimizer object for the specified type of extremum.

	Name	Description
	ConvergenceTests	Gets the collection of convergence tests for the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	DerivativeOfObjectiveFunction	Gets or sets the derivative of the objective function. (Inherited from OneDimensionalOptimizer.)
	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.)
	Extremum	Gets the approximation to the extremum after the algorithm has run. (Inherited from OneDimensionalOptimizer.)
	ExtremumType	Gets or sets the type of extremum. (Inherited from OneDimensionalOptimizer.)
	HasSharedDegreeOfParallelism	Indicates whether the degree of parallelism is a property that is shared across instances. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	IsBracketValid	Gets whether the algorithm's current bracket is valid. (Inherited from OneDimensionalOptimizer.)
	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 OneDimensionalOptimizer.)
	ObjectiveFunctionWithDerivative	Gets or sets a function that computes the value of the objective function and its derivative. (Inherited from OneDimensionalOptimizer.)
	ParallelOptions	Gets or sets the configuration for the parallel behavior of the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	Result	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	SolutionReport	Gets the result of an algorithm after it has executed. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	SolutionTest	Gets the convergence test that uses the solution of the optimization. (Inherited from OneDimensionalOptimizer.)
	Status	Gets the AlgorithmStatus following an execution of the algorithm. (Inherited from ManagedIterativeAlgorithmT, TError, TReport.)
	SymbolicObjectiveFunction	Gets or sets the objective function. (Inherited from OneDimensionalOptimizer.)
	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 the value of the objective function at the approximation to the extremum after the algorithm has run. (Inherited from OneDimensionalOptimizer.)

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	FindBracket	Finds an interval that brackets the extremum, starting from the interval [0,1]. (Inherited from OneDimensionalOptimizer.)
	FindBracket(Double)	Finds an interval that brackets the extremum, starting from an interval of unit width centered around the specified point. (Inherited from OneDimensionalOptimizer.)
	FindBracket(Double, Double)	Finds an interval that brackets the extremum, starting from an interval with the specified bounds. (Inherited from OneDimensionalOptimizer.)
	FindBracket(Double, Double, Double)	Finds an interval that brackets the extremum, starting from an interval with the specified bounds and interior point. (Inherited from OneDimensionalOptimizer.)
	FindExtremum	Searches for an extremum. (Inherited from OneDimensionalOptimizer.)
	FindMaximum(FuncDouble, Double, Double)	Computes a maximum of the specified function. (Inherited from OneDimensionalOptimizer.)
	FindMaximum(FuncDouble, Double, Double, Double)	Computes a maximum of the specified function. (Inherited from OneDimensionalOptimizer.)
	FindMinimum(FuncDouble, Double, Double)	Computes a minimum of the specified function. (Inherited from OneDimensionalOptimizer.)
	FindMinimum(FuncDouble, Double, Double, Double)	Computes a minimum of the specified function. (Inherited from OneDimensionalOptimizer.)
	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 BrentOptimizer class to find a minimum or maximum of a function when the derivative of the objective function is not available or very expensive to calculate.

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) or FindMinimum(FuncDouble, 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.

The algorithm uses Brent's original algorithm. In each iteration of the location phase, either a Golden Section step is taken, or a new approximation is calculated using quadratic or cubic interpolation. This method is the most robust method available for optimization in one dimension.

Reference