TrustRegionMinimizer Class

Class TrustRegionMinimizer solves both constrained and unconstrained nonlinear least squares problems using the Trust Region method.

Inheritance Hierarchy

SystemObject
CenterSpace.NMath.CoreTrustRegionMinimizer

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.3

Syntax

C++

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[SerializableAttribute]
public class TrustRegionMinimizer : IBoundedNonlinearLeastSqMinimizer, 
	INonlinearLeastSqMinimizer, ICloneable

<SerializableAttribute>
Public Class TrustRegionMinimizer
	Implements IBoundedNonlinearLeastSqMinimizer, INonlinearLeastSqMinimizer, ICloneable

[SerializableAttribute]
public ref class TrustRegionMinimizer : IBoundedNonlinearLeastSqMinimizer, 
	INonlinearLeastSqMinimizer, ICloneable

[<SerializableAttribute>]
type TrustRegionMinimizer =  
    class
        interface IBoundedNonlinearLeastSqMinimizer
        interface INonlinearLeastSqMinimizer
        interface ICloneable
    end

The TrustRegionMinimizer type exposes the following members.

Constructors

	Name	Description
	TrustRegionMinimizer	Default constructor.
	TrustRegionMinimizer(Double)	Constructs a TrustRegionMinimizer instance with the given error tolerance.
	TrustRegionMinimizer(Int32)	Constructs a TrustRegionMinimizer instance with the given maximum number of iterations.
	TrustRegionMinimizer(Double, Int32)	Constructs a TrustRegionMinimizer instance with the given maximum number of iterations.

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Properties

	Name	Description
	DefaultMaxIterations	Gets and sets the default maximum number of iterations.
	DefaultTolerance	Gets and sets the default error tolerance.
	FinalResidual	Gets the residual associated with the last computed solution.
	InitialResidual	Gets the residual associated with the starting point.
	InitialStepBound	Gets and sets the initial step bound. In most cases this should be between 0.1 and 100.0.
	Iterations	Gets the number of iterations used in the estimate of the mimimum just computed.
	MaxIterations	Gets and sets the maximum number of iterations used in computing minima estimates.
	MaxIterationsMet	Returns true if the minimum just computed stopped because the maximum number of iterations was reached; otherwise, false.
	MaxTrialIterations	Gets and sets the maximum number of iterations of trial step calculation.
	StopCriterion	The reason for stopping.
	ToleranceFunctionValue	Gets and sets the tolerance used to check the function value.
	ToleranceImprovement	Gets and sets the tolerance used to check the improvement between steps.
	ToleranceJacobian	Gets and sets the tolerance used to check the Jacobian.
	ToleranceTrialStep	Gets and sets the tolerance used to check the trial step.
	ToleranceTrustRegionArea	Gets and sets the tolerance used to check the trust region area.

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Methods

	Name	Description
	Clone	Creates a deep copy of self.
	Minimize(DoubleMultiVariableFunction, DoubleVector)	Minimizes the given function near the given starting point.
	Minimize(FuncDouble, Double, DoubleVector, Int32)	Minimizes the given function near the given starting point.
	Minimize(FuncDoubleVector, DoubleVector, DoubleVector, Int32)	Minimizes the given function near the given starting point.
	Minimize(FuncDouble, Double, DoubleVector, Int32, FuncDouble, Double)	Minimizes the given function near the given starting point, using the given array of partial derivatives.
	Minimize(DoubleMultiVariableFunction, DoubleVector, DoubleVector, DoubleVector)	Minimizes the given function near the given starting point, within the specified contraints.
	Minimize(FuncDoubleVector, DoubleVector, DoubleVector, Int32, FuncDoubleVector, DoubleVector)	Minimizes the given function near the given starting point, using the given array of partial derivatives.
	Minimize(FuncDouble, Double, DoubleVector, Int32, DoubleVector, DoubleVector)	Minimizes the given function near the given starting point, within the specified contraints.
	Minimize(FuncDoubleVector, DoubleVector, DoubleVector, Int32, DoubleVector, DoubleVector)	Minimizes the given function near the given starting point, within the specified contraints.
	Minimize(FuncDouble, Double, DoubleVector, Int32, FuncDouble, Double, DoubleVector, DoubleVector)	Minimizes the given function near the given starting point, within the specified contraints, and using the given array of partial derivatives.
	Minimize(FuncDoubleVector, DoubleVector, DoubleVector, Int32, FuncDoubleVector, DoubleVector, DoubleVector, DoubleVector)	Minimizes the given function near the given starting point, within the specified contraints, and using the given array of partial derivatives.
	SetAllTolerances	Sets all the error tolerances used in computing minima estimates.

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Fields

	Name	Description
	DEFAULT_MAX_ITER	The default maximum number of iterations.
	DEFAULT_TOLERANCE	The default error tolerance.

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Remarks

Solving a nonlinear least squares problem involves finding the best approximation to vector yValues with a model function that has nonlinear dependence on variables x, by minimizing the sum of squares of residuals.
The Trust Region method maintains a region around the current search point where a quadratic model is "trusted" to be correct. If an adequate model of the objective function is found within the trust region, the region is expanded. Otherwise, the region is contracted.
The Trust Region algorithm requires the partial derivatives of the function, but a numerical approximation may be used if the closed form is not available.
For example, the following code minimizes a function, without constraints, using a numerical approximation of the partial derivatives, and starting at point (3.0, -1.0, 0.0, 1.0);

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TrustRegionMinimizer minimizer = new TrustRegionMinimizer();

NMathFunctions.DoubleVectorDoubleVectorFunction f = delegate(DoubleVector x)
{
  DoubleVector fx = new DoubleVector(x.Length);
  for (int i = 0; i < (x.Length) / 4; i++)
  {
    fx[4 * i] = x[4 * i] + 10.0 * x[4 * i + 1];
    fx[4 * i + 1] = 2.2360679774997896964091736687313 * (x[4 * i + 2] - x[4 * i + 3]);
    fx[4 * i + 2] = (x[4 * i + 1] - 2.0 * x[4 * i + 2]) * (x[4 * i + 1] - 2.0 * x[4 * i + 2]);
    fx[4 * i + 3] = 3.1622776601683793319988935444327 * (x[4 * i] - x[4 * i + 3]) * (x[4 * i] - x[4 * i + 3]);
  }
  return fx;
};

DoubleVector start = new DoubleVector("3.0 -1.0 0.0 1.0");
int ydim = 4;
DoubleVector solution = minimizer.Minimize(f, start, ydim);

Console.WriteLine("solution = " + solution);
Console.WriteLine("iterations = " + minimizer.Iterations);
Console.WriteLine("initial error = " + minimizer.InitialResidual);
Console.WriteLine("final error = " + minimizer.FinalResidual);
Console.WriteLine("stop criterion = " + minimizer.StopCriterion);

Reference

CenterSpace.NMath.Core Namespace