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Showing content from http://accord-framework.net/docs/html/T_Accord_Math_Optimization_ConjugateGradient.htm below:

Conjugate Gradient (CG) optimization method.

Accord.Math (in Accord.Math.dll) Version: 3.8.0

public class ConjugateGradient : BaseGradientOptimizationMethod, 
	IGradientOptimizationMethod, IOptimizationMethod, IOptimizationMethod<double[], double>, 
	IGradientOptimizationMethod<double[], double>, IFunctionOptimizationMethod<double[], double>, 
	IOptimizationMethod<ConjugateGradientCode>, IOptimizationMethod<double[], double, ConjugateGradientCode>, 
	ISupportsCancellation

Public Class ConjugateGradient
	Inherits BaseGradientOptimizationMethod
	Implements IGradientOptimizationMethod, IOptimizationMethod, IOptimizationMethod(Of Double(), Double), 
	IGradientOptimizationMethod(Of Double(), Double), IFunctionOptimizationMethod(Of Double(), Double), 
	IOptimizationMethod(Of ConjugateGradientCode), IOptimizationMethod(Of Double(), Double, ConjugateGradientCode), 
	ISupportsCancellation

The ConjugateGradient type exposes the following members.

Gets the number of function evaluations performed in the last call to

.

Gets or sets the function to be optimized.

Gets or sets a function returning the gradient vector of the function to be optimized for a given value of its free parameters.

Gets the number of iterations performed in the last call to

.

Gets or sets the maximum number of iterations to be performed during optimization. Default is 0 (iterate until convergence).

Gets or sets the conjugate gradient update method to be used during optimization.

Gets the number of variables (free parameters) in the optimization problem.

Gets the number of linear searches performed in the last call to

.

Gets the current solution found, the values of the parameters which optimizes the function.

Get the exit code returned in the last call to the

or

methods.

Gets or sets a cancellation token that can be used to stop the learning algorithm while it is running.

Gets or sets the relative difference threshold to be used as stopping criteria between two iterations. Default is 0 (iterate until convergence).

Gets the output of the function at the current

.

Occurs when progress is made during the optimization.

Checks whether an object implements a method with the given name.

Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.

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.

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.

In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive- definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too large to be handled by direct methods. Such systems often arise when numerically solving partial differential equations. The nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization (Wikipedia, 2011).

T

The framework implementation of this method is based on the original FORTRAN source code by Jorge Nocedal (see references below). The original FORTRAN source code of CG+ (for large scale unconstrained problems) is available at http://users.eecs.northwestern.edu/~nocedal/CG+.html and had been made freely available for educational or commercial use. The original authors expect that all publications describing work using this software quote the (Gilbert and Nocedal, 1992) reference given below.

References:

• J. C. Gilbert and J. Nocedal. Global Convergence Properties of Conjugate Gradient Methods for Optimization, (1992) SIAM J. on Optimization, 2, 1.
• Wikipedia contributors, "Nonlinear conjugate gradient method," Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Nonlinear_conjugate_gradient_method (accessed December 22, 2011).
• Wikipedia contributors, "Conjugate gradient method," Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Conjugate_gradient_method (accessed December 22, 2011).

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