PowellOptimizer Class

Implements Powell's modified multidimensional optimization method.

Definition

Namespace: Extreme.Mathematics.Optimization
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
C#
public sealed class PowellOptimizer : DirectionalOptimizer
Inheritance
Object  →  ManagedIterativeAlgorithm<Vector<Double>, Double, OptimizationSolutionReport>  →  MultidimensionalOptimizer  →  DirectionalOptimizer  →  PowellOptimizer

Remarks

Use the PowellOptimizer class to find an extremum of a multivariate function using Powell's direction set method. The method is useful when the gradient of the objective function is not available. Still, this method is usually less efficient than either a quasi-Newton or a full conjugate gradient method with a numerical approximation of the gradient. It is here mostly for its historical importance.

The objective function must be supplied as a multivariate function delegate to the ObjectiveFunction property. The gradient of the objective function can be supplied either as a multivariate function returning a vector delegate (by setting the GradientFunction property), or a multivariate function returning a vector in its second argument delegate (by setting the FastGradientFunction property). The latter has the advantage that the same Vector instance is reused to hold the result.

Before the algorithm is run, you must set the InitialGuess property to a vector that contains an initial estimate for the extremum. The ExtremumType property specifies whether a minimum or a maximum of the objective function is desired.

The FindExtremum() method performs the actual search for an extremum, and returns a Vector containing the best approximation. The Extremum property also 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 the objective function is not bounded.

The algorithm has two convergence tests. By default, the algorithm terminates when either of these is satisfied. You can deactivate either test by setting its Enabled property to false. If both tests are deactivated, then the algorithm always terminates when the maximum number of iterations or function evaluations is reached.

The first test is based on the uncertainty in the location of the approximate extremum. The SolutionTest property returns a VectorConvergenceTest<T> object that allows you to specify the desired Tolerance and specific ConvergenceCriterion. See the VectorConvergenceTest<T> class for details on how to further customize this test.

The second test is based on the change in value of the objective function at the approximate extremum. The test is successful when the change of the value of the objective function is within the tolerance. Care should be taken with this test. When the tolerance is too large, the algorithm will terminate prematurely. The ValueTest property returns a SimpleConvergenceTest<T> object that can be used to customize the test.

A third test, based on the value of the gradient at the approximate extremum, is exposed through the GradientTest property. However, this test does not apply to Powell's method, and it's Enabled property is set to false before the algorithm is executed.

Constructors

PowellOptimizer Constructs a new PowellOptimizer object.

Properties

ConvergenceTests Gets the collection of convergence tests for the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
CurrentDirection Gets or sets the current search direction.
(Inherited from DirectionalOptimizer)
Dimensions Gets or sets the number of dimensions of the optimization problem.
(Inherited from MultidimensionalOptimizer)
EstimatedError Gets a value indicating the size of the absolute error of the result.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
EvaluationsNeeded Gets the number of evaluations needed to execute the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Extremum Gets or sets the current best approximation to the extremum.
(Inherited from MultidimensionalOptimizer)
ExtremumType Gets or sets the type of extremum.
(Inherited from MultidimensionalOptimizer)
FastGradientFunction Gets or sets the function that computes the gradient of the objective funciton.
(Inherited from MultidimensionalOptimizer)
GradientEvaluationsNeeded Gets the number of evaluations of the gradient of the objective function.
(Inherited from MultidimensionalOptimizer)
GradientFunction Gets or sets the function that computes the gradient of the objective funciton.
(Inherited from MultidimensionalOptimizer)
GradientTest Gets the VectorConvergenceTest<T> that uses the gradient of the objective function.
(Inherited from MultidimensionalOptimizer)
GradientVector Gets or sets the current value of the gradient.
(Inherited from MultidimensionalOptimizer)
HasSharedDegreeOfParallelism Indicates whether the degree of parallelism is a property that is shared across instances.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
InitialGuess Gets or sets the initial value for the iteration.
(Inherited from MultidimensionalOptimizer)
IterationsNeeded Gets the number of iterations needed by the algorithm to reach the desired accuracy.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
LineSearch Gets or sets the algorithm used to perform a line search.
(Inherited from DirectionalOptimizer)
MaxDegreeOfParallelism Gets or sets the maximum degree of parallelism enabled by this instance.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MaxEvaluations Gets or sets the maximum number of evaluations during the calculation.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MaxIterationsGets or sets the maximum number of iterations to use when approximating the roots of the target function.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
MinIterations Gets or sets the minimum iterations that have to be performed.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ObjectiveFunction Gets or sets the objective function.
(Inherited from MultidimensionalOptimizer)
ObjectiveFunctionWithGradient Gets or sets a function that evaluates the value and gradient of the objective function.
(Inherited from MultidimensionalOptimizer)
ParallelOptions Gets or sets the configuration for the parallel behavior of the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
Result Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
SolutionReport Gets the result of an algorithm after it has executed.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
SolutionTest Gets the VectorConvergenceTest<T> that uses the approximate solution.
(Inherited from MultidimensionalOptimizer)
Status Gets the AlgorithmStatus following an execution of the algorithm.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
SymbolicObjectiveFunction Gets or sets the objective function.
(Inherited from MultidimensionalOptimizer)
ThrowExceptionOnFailure Gets or sets a value indicating whether to throw an exception when the algorithm fails to converge.
(Inherited from ManagedIterativeAlgorithm<T, TError, TReport>)
ValueAtExtremum Gets or sets the current value of the objective function.
(Inherited from MultidimensionalOptimizer)
ValueTest Gets the SimpleConvergenceTest<T> that uses the value of the target functions.
(Inherited from MultidimensionalOptimizer)

Methods

EqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
FindExtremum Searches for an extremum.
(Inherited from MultidimensionalOptimizer)
GetHashCodeServes as the default hash function.
(Inherited from Object)
GetTypeGets the Type of the current instance.
(Inherited from Object)
ToStringReturns a string that represents the current object.
(Inherited from Object)

See Also