Click or drag to resize
Accord.NET (logo)

TrustRegionNewtonMethod Class

Simplified Trust Region Newton Method (TRON) for non-linear optimization.
Inheritance Hierarchy
SystemObject
  Accord.Math.OptimizationBaseOptimizationMethod
    Accord.Math.OptimizationBaseGradientOptimizationMethod
      Accord.Math.OptimizationTrustRegionNewtonMethod

Namespace:  Accord.Math.Optimization
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.5.0
Syntax
public class TrustRegionNewtonMethod : BaseGradientOptimizationMethod
Request Example View Source

The TrustRegionNewtonMethod type exposes the following members.

Constructors
Properties
  NameDescription
Public propertyFunction
Gets or sets the function to be optimized.
(Inherited from BaseOptimizationMethod.)
Public propertyGradient
Gets or sets a function returning the gradient vector of the function to be optimized for a given value of its free parameters.
(Inherited from BaseGradientOptimizationMethod.)
Public propertyHessian
Gets or sets the Hessian estimation function.
Public propertyMaxIterations
Gets or sets the maximum number of iterations that should be performed until the algorithm stops. Default is 1000.
Public propertyNumberOfVariables
Gets the number of variables (free parameters) in the optimization problem.
(Inherited from BaseOptimizationMethod.)
Public propertySolution
Gets the current solution found, the values of the parameters which optimizes the function.
(Inherited from BaseOptimizationMethod.)
Public propertyToken
Gets or sets a cancellation token that can be used to stop the learning algorithm while it is running.
(Inherited from BaseOptimizationMethod.)
Public propertyTolerance
Gets or sets the tolerance under which the solution should be found. Default is 0.1.
Public propertyValue
Gets the output of the function at the current Solution.
(Inherited from BaseOptimizationMethod.)
Top
Methods
  NameDescription
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodMaximize
Finds the maximum value of a function. The solution vector will be made available at the Solution property.
(Inherited from BaseGradientOptimizationMethod.)
Public methodMaximize(Double)
Finds the maximum value of a function. The solution vector will be made available at the Solution property.
(Inherited from BaseOptimizationMethod.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodMinimize
Finds the minimum value of a function. The solution vector will be made available at the Solution property.
(Inherited from BaseGradientOptimizationMethod.)
Public methodMinimize(Double)
Finds the minimum value of a function. The solution vector will be made available at the Solution property.
(Inherited from BaseOptimizationMethod.)
Protected methodOnNumberOfVariablesChanged
Called when the NumberOfVariables property has changed.
(Inherited from BaseOptimizationMethod.)
Protected methodOptimize
Implements the actual optimization algorithm. This method should try to minimize the objective function.
(Overrides BaseOptimizationMethodOptimize.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Top
Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToTOverloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
Public Extension MethodToTOverloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by Matrix.)
Top
Remarks

Trust region is a term used in mathematical optimization to denote the subset of the region of the objective function to be optimized that is approximated using a model function (often a quadratic). If an adequate model of the objective function is found within the trust region then the region is expanded; conversely, if the approximation is poor then the region is contracted. Trust region methods are also known as restricted step methods.

The fit is evaluated by comparing the ratio of expected improvement from the model approximation with the actual improvement observed in the objective function. Simple thresholding of the ratio is used as the criteria for expansion and contraction—a model function is "trusted" only in the region where it provides a reasonable approximation.

Trust region methods are in some sense dual to line search methods: trust region methods first choose a step size (the size of the trust region) and then a step direction while line search methods first choose a step direction and then a step size.

This class implements a simplified version of Chih-Jen Lin and Jorge Moré's TRON, a trust region Newton method for the solution of large bound-constrained optimization problems. This version was based upon liblinear's implementation.

References:

See Also