QuasiNewtonOptimizer Class

public sealed class QuasiNewtonOptimizer : DirectionalOptimizer

Public NotInheritable Class QuasiNewtonOptimizer
	Inherits DirectionalOptimizer

public ref class QuasiNewtonOptimizer sealed : public DirectionalOptimizer

[<SealedAttribute>]
type QuasiNewtonOptimizer =  
    class
        inherit DirectionalOptimizer
    end

The QuasiNewtonOptimizer type exposes the following members.

	Name	Description
	QuasiNewtonOptimizer	Constructs a new QuasiNewtonOptimizer object.
	QuasiNewtonOptimizer(QuasiNewtonMethod)	Constructs a new QuasiNewtonOptimizer object.

	Name	Description
	ConvergenceTests	Gets the collection of convergence tests for the algorithm. (Inherited from ManagedIterativeAlgorithmT, 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 ManagedIterativeAlgorithmT, TError, TReport.)
	EvaluationsNeeded	Gets the number of evaluations needed to execute the algorithm. (Inherited from ManagedIterativeAlgorithmT, 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 VectorConvergenceTestT 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 ManagedIterativeAlgorithmT, 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 ManagedIterativeAlgorithmT, 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 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.)
	Method	Gets or sets the method used to update the conjugate gradient direction.
	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 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 ManagedIterativeAlgorithmT, TError, TReport.)
	RestartIterations	Gets or sets a value that indicates when the Hessian approximation should be restarted from a diagonal matrix.
	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 VectorConvergenceTestT that uses the approximate solution. (Inherited from MultidimensionalOptimizer.)
	Status	Gets the AlgorithmStatus following an execution of the algorithm. (Inherited from ManagedIterativeAlgorithmT, 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 ManagedIterativeAlgorithmT, TError, TReport.)
	ValueAtExtremum	Gets or sets the current value of the objective function. (Inherited from MultidimensionalOptimizer.)
	ValueTest	Gets the SimpleConvergenceTestT that uses the value of the target functions. (Inherited from MultidimensionalOptimizer.)

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	FindExtremum	Searches for an extremum. (Inherited from MultidimensionalOptimizer.)
	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.)

Use the QuasiNewtonOptimizer class to find an extremum of a multivariate function using a quasi-Newton method. Two variations of this method are available: the BFGS method of Broyden, Fletcher, Goldfarb and Shanno, and the DFP method of Davison, Fletcher and Powell. The default is the BFGS method.

A quasi-Newton method is the preferred method for smaller problems when the gradient of the objective function is available. For large problems, the Conjugate Gradient method is usually more efficient.

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.

Sometimes, the gradient function is not available, or is very expensive to calculate. In such instances, a numerical approximation may work better.

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 three convergence tests. By default, the algorithm terminates when either of these is satisfied. You can deactivate either test by setting its Enabled property to . 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 VectorConvergenceTestT object that allows you to specify the desired Tolerance and specific ConvergenceCriterion. See the VectorConvergenceTestT 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 SimpleConvergenceTestT object that can be used to customize the test.

The third test is based on the value of the gradient at the approximate extremum. The GradientTest property returns a VectorConvergenceTestT object that can be used to customize the test. By default, the error is set to the component with the largest absolute value.

Reference