TrustRegionNewtonMethod Class 
Namespace: Accord.Math.Optimization
The TrustRegionNewtonMethod type exposes the following members.
Name  Description  

TrustRegionNewtonMethod(Int32) 
Creates a new ResilientBackpropagation function optimizer.
 
TrustRegionNewtonMethod(Int32, FuncDouble, Double, FuncDouble, Double, FuncDouble, Double) 
Creates a new ResilientBackpropagation function optimizer.

Name  Description  

Function 
Gets or sets the function to be optimized.
(Inherited from BaseOptimizationMethod.)  
Gradient 
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.)  
Hessian 
Gets or sets the Hessian estimation function.
 
MaxIterations 
Gets or sets the maximum number of iterations that should
be performed until the algorithm stops. Default is 1000.
 
NumberOfVariables 
Gets the number of variables (free parameters)
in the optimization problem.
(Inherited from BaseOptimizationMethod.)  
Solution 
Gets the current solution found, the values of
the parameters which optimizes the function.
(Inherited from BaseOptimizationMethod.)  
Token 
Gets or sets a cancellation token that can be used to
stop the learning algorithm while it is running.
(Inherited from BaseOptimizationMethod.)  
Tolerance 
Gets or sets the tolerance under which the
solution should be found. Default is 0.1.
 
Value 
Gets the output of the function at the current Solution.
(Inherited from BaseOptimizationMethod.) 
Name  Description  

Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
Maximize 
Finds the maximum value of a function. The solution vector
will be made available at the Solution property.
(Inherited from BaseGradientOptimizationMethod.)  
Maximize(Double) 
Finds the maximum value of a function. The solution vector
will be made available at the Solution property.
(Inherited from BaseOptimizationMethod.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
Minimize 
Finds the minimum value of a function. The solution vector
will be made available at the Solution property.
(Inherited from BaseGradientOptimizationMethod.)  
Minimize(Double) 
Finds the minimum value of a function. The solution vector
will be made available at the Solution property.
(Inherited from BaseOptimizationMethod.)  
OnNumberOfVariablesChanged 
Called when the NumberOfVariables property has changed.
(Inherited from BaseOptimizationMethod.)  
Optimize 
Implements the actual optimization algorithm. This
method should try to minimize the objective function.
(Overrides BaseOptimizationMethodOptimize.)  
ToString  Returns a string that represents the current object. (Inherited from Object.) 
Name  Description  

HasMethod 
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)  
IsEqual 
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.)  
To(Type)  Overloaded.
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.)  
ToT  Overloaded.
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.) 
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 ChihJen Lin and Jorge Moré's TRON, a trust region Newton method for the solution of large boundconstrained optimization problems. This version was based upon liblinear's implementation.
References: