Represents a one-dimensional optimizer based on Brent's algorithm using derivatives.
SystemObject Extreme.Mathematics.AlgorithmsManagedIterativeAlgorithmDouble,
Double,
SolutionReportDouble,
Double Extreme.Mathematics.AlgorithmsManagedIterativeAlgorithmDouble Extreme.Mathematics.OptimizationOneDimensionalOptimizer Extreme.Mathematics.OptimizationBrentDerivativeOptimizer
Namespace: Extreme.Mathematics.OptimizationAssembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 6.0.16073.0 (6.0.16312.0)
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
The BrentDerivativeOptimizer type exposes the following members.
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| 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 a hash function for a particular type. (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.) |
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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(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 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 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.
Numerical Libraries
Supported in: 6.0, 5.x, 4.x
Reference