Represents a one-dimensional optimizer based on Brent's algorithm.
SystemObject Extreme.Mathematics.AlgorithmsManagedIterativeAlgorithmDouble,
Double,
SolutionReportDouble,
Double Extreme.Mathematics.AlgorithmsManagedIterativeAlgorithmDouble Extreme.Mathematics.OptimizationOneDimensionalOptimizer Extreme.Mathematics.OptimizationBrentOptimizer
Namespace: Extreme.Mathematics.OptimizationAssembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 6.0.16073.0 (6.0.16312.0)
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.
Top
Top
| 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.) |
Top
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 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.
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.
Numerical Libraries
Supported in: 6.0, 5.x, 4.x
Reference