FanChenLinQuadraticOptimization Class

General Sequential Minimal Optimization algorithm for Quadratic Programming problems.

Inheritance Hierarchy

SystemObject
Accord.Math.OptimizationFanChenLinQuadraticOptimization

Namespace: Accord.Math.Optimization
Assembly: Accord.Math (in Accord.Math.dll) Version: 3.8.0

Syntax

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public class FanChenLinQuadraticOptimization : IOptimizationMethod, 
	IOptimizationMethod<double[], double>

Public Class FanChenLinQuadraticOptimization
	Implements IOptimizationMethod, IOptimizationMethod(Of Double(), Double)

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The FanChenLinQuadraticOptimization type exposes the following members.

Constructors

	Name	Description
	FanChenLinQuadraticOptimization(Int32, FuncInt32, Int32, Int32, Double, Double)	Initializes a new instance of the FanChenLinQuadraticOptimization class.
	FanChenLinQuadraticOptimization(Int32, FuncInt32, Int32, Int32, Double, Double, Double, Int32)	Initializes a new instance of the FanChenLinQuadraticOptimization class.

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Properties

	Name	Description
	NumberOfVariables	Gets the number of variables (free parameters) in the optimization problem. In a SVM learning problem, this is the number of samples in the learning dataset.
	Rho	Gets the threshold (bias) value for a SVM trained using this method.
	Shrinking	Gets or sets a value indicating whether shrinking heuristics should be used. Default is false.
	Solution	Gets the current solution found, the values of the parameters which optimizes the function.
	Token	Gets or sets a cancellation token that can be used to stop the learning algorithm while it is running.
	Tolerance	Gets or sets the precision tolerance before the method stops. Default is 0.001.
	UpperBounds	Gets the upper bounds for the optimization problem. In a SVM learning problem, this would be the capacity limit for each Lagrange multiplier (alpha) in the machine. The default is to use a vector filled with 1's.
	Value	Gets the output of the function at the current Solution.

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Methods

	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	Not supported.
	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.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Extension Methods

	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.)

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Remarks

This class implements the same optimization method found in LibSVM. It can be used to solve quadratic programming problems where the quadratic matrix Q may be too large to fit in memory.

The method is described in Fan et al., JMLR 6(2005), p. 1889--1918. It solves the minimization problem:

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min 0.5(\alpha^T Q \alpha) + p^T \alpha

  y^T \alpha = \delta
  y_i = +1 or -1
  0 <= alpha_i <= C_i

Given Q, p, y, C, and an initial feasible point \alpha, where l is the size of vectors and matrices and eps is the stopping tolerance.

Reference

Accord.Math.Optimization Namespace