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.Optimization
Assembly:
Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.1
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.
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| 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 | (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.) |
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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 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.) |
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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