General Sequential Minimal Optimization algorithm for Quadratic Programming problems.
Inheritance Hierarchy
SystemObject

Namespace:  Accord.Math.Optimization
Assembly:  Accord.Math (in Accord.Math.dll) Version: 3.8.0
Syntax
public class FanChenLinQuadraticOptimization : IOptimizationMethod,
IOptimizationMethod<double[], double>

The FanChenLinQuadraticOptimization type exposes the following members.

Constructors
Properties
NameDescription
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
NameDescription
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
NameDescription
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.)
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.)
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:

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.