BrentDerivativeOptimizer Class

public sealed class BrentDerivativeOptimizer : OneDimensionalOptimizer

Public NotInheritable Class BrentDerivativeOptimizer
	Inherits OneDimensionalOptimizer

public ref class BrentDerivativeOptimizer sealed : public OneDimensionalOptimizer

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

Inheritance

Object  →  ManagedIterativeAlgorithm<Double, Double, SolutionReport<Double, Double>>  →  ManagedIterativeAlgorithm<Double>  →  OneDimensionalOptimizer  →  BrentDerivativeOptimizer

Use the BrentDerivativeOptimizer class to find an extremum of a function when its derivative function is known. This method is often preferred, especially when the derivative function is easier to evaluate than the objective function itself.

The ObjectiveFunction property must be set to a function of one variable that evaluates the objective function. The DerivativeOfObjectiveFunction property must be set to a function of one variable that evaluates the derivative of 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() 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(Func<Double, Double>, Double) or FindMinimum(Func<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 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 SimpleConvergenceTest<T> object that allows you to specify the desired Tolerance and specific ConvergenceCriterion.

The algorithm uses a variation of Brent's algorithm that uses the value of the derivative to make decisions during the location phase. Except in cases where the function value is more expensive to calculate than the derivative, this method does not have a real advantage over the method that does not use derivatives.

Reference