Namespace List

The namespaces specified in this document are:

Namespace	Assembly
Net.Kniaz.Optimization.QuasiNewton.Tests	Net.Kniaz.Optimization
Net.Kniaz.Optimization	Net.Kniaz.Optimization
Net.Kniaz.Optimization.NonGradient.Tests	Net.Kniaz.Optimization
Net.Kniaz.Optimization.QuasiNewton	Net.Kniaz.Optimization
Net.Kniaz.Math.DFP	Net.Kniaz.Optimization
Net.Kniaz.Optimization.NonGradient	Net.Kniaz.Optimization

Namespace : Net.Kniaz.Math.DFP

Net.Kniaz.Math.DFP Type List

Classes

Type	Summary
LinearSearch	Summary description for Class1.

Net.Kniaz.Math.DFP Classes

LinearSearch Class

Summary

public class LinearSearch

Summary description for Class1.

Constructor Members

Name	Access	Summary
LinearSearch()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
Search() : Void	public

Namespace : Net.Kniaz.Optimization.QuasiNewton

Net.Kniaz.Optimization.QuasiNewton Type List

Classes

Type	Summary
BFGS	Summary description for QuasiNewtonOptimization.
DFP	Summary description for DFP.
LineSearch	Summary description for LineSearch.
OneDWrapper	Summary description for OneDWrapper.
Optimizer	Summary description for Optimizer.

Net.Kniaz.Optimization.QuasiNewton Classes

Optimizer Class

Summary

public abstract class Optimizer

Summary description for Optimizer.

Constructor Members

Name	Access	Summary
Optimizer()	public

Field Members

Name	Access	Summary
_alpha : Double	protected
_curIter : Int32	protected
_epsilon : Double	protected
_f : IGradientFunction	protected
_hessian : GeneralMatrix	protected
_initial : Double[]	protected
_itMax : Int32	protected
_nDim : Int32	protected
_step : Double	protected
_xCurrent : Double[]	protected

Property Members

Name	Access	Summary
Iteration : Int32	public
Minimum : Double[]	public

Method Members

Name	Access	Summary
CalculateNextHessianApproximation() : GeneralMatrix	protected
Diff() : Double	protected
FindMinimum() : Void	public

BFGS Class

Summary

public class BFGS : Optimizer

Summary description for QuasiNewtonOptimization.

Constructor Members

Name	Access	Summary
BFGS()	public

Field Members

Name	Access	Summary
_alpha : Double	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_curIter : Int32	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_epsilon : Double	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_f : IGradientFunction	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_hessian : GeneralMatrix	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_initial : Double[]	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_itMax : Int32	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_nDim : Int32	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_step : Double	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_xCurrent : Double[]	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)

Property Members

Name	Access	Summary
Iteration : Int32	public	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
Minimum : Double[]	public	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)

Method Members

Name	Access	Summary
CalculateNextHessianApproximation() : GeneralMatrix	protected
Diff() : Double	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
FindMinimum() : Void	public	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)

DFP Class

Summary

public class DFP : Optimizer

Summary description for DFP.

Constructor Members

Name	Access	Summary
DFP()	public

Field Members

Name	Access	Summary
_alpha : Double	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_curIter : Int32	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_epsilon : Double	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_f : IGradientFunction	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_hessian : GeneralMatrix	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_initial : Double[]	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_itMax : Int32	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_nDim : Int32	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_step : Double	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
_xCurrent : Double[]	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)

Property Members

Name	Access	Summary
Iteration : Int32	public	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
Minimum : Double[]	public	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)

Method Members

Name	Access	Summary
CalculateNextHessianApproximation() : GeneralMatrix	protected
Diff() : Double	protected	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)
FindMinimum() : Void	public	(from Net.Kniaz.Optimization.QuasiNewton.Optimizer)

LineSearch Class

Summary

public class LineSearch

Summary description for LineSearch.

Constructor Members

Name	Access	Summary
LineSearch()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
FindMinimumViaBrent() : Int32	public	Finds minimum via a Brent Method: http://mathworld.wolfram.com/BrentsMethod.html
FindMinimumViaGoldenSection() : Int32	public	Finds minimum via gold section search. x1 must be between x0 and x2
FindMinInterval() : Int32	public

OneDWrapper Class

Summary

public class OneDWrapper : Net.Kniaz.Optimization.IOneDFunction

Summary description for OneDWrapper.

Constructor Members

Name	Access	Summary
OneDWrapper()	public

Method Members

Name	Access	Summary
GetVal() : Double	public

Namespace : Net.Kniaz.Optimization.QuasiNewton.Tests

Net.Kniaz.Optimization.QuasiNewton.Tests Type List

Classes

Type	Summary
Banana	Initializes a new instance of the class.
BrentTests	Testing linear minimum search using Brent method.
Derivatives	Initializes a new instance of the class.
DFPTests	TestDFP.
GoldenTests	Testing one dimensional minimum using the Golden Section Algorithm
IntervalTests	Testing of the interval barcketing algorithm
Parabola	Initializes a new instance of the class.
TestFunction	Initializes a new instance of the class.

Net.Kniaz.Optimization.QuasiNewton.Tests Classes

BrentTests Class

Summary

public class BrentTests

Testing linear minimum search using Brent method.

Constructor Members

Name	Access	Summary
BrentTests()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
MinBrent1() : Void	public	Testing using function from the interval test function. Global Min is at x = -1.364641. We are starting with finding the bracket at 10 with step 1. Bracket function returns -4.764, -0.529, 6.326. These are fed to the 1D min function
MinBrent2() : Void	public	This time the start is around the local minimum so the search should converge around local minimum
MinBrent3() : Void	public	Tests regular parabola with a min of -0.75. Start the test coming from negative direction
MinBrent4() : Void	public	Testing the same parabola as in the previous function but coming from the far positive direction
MinBrent5() : Void	public	testing a parabola added to an exp

TestFunction Class

Summary

public class TestFunction : RealFunction, Net.Kniaz.Optimization.IGradientFunction, Net.Kniaz.Optimization.IFunction

Constructor Members

Name	Access	Summary
TestFunction()	public	Initializes a new instance of the class.

Property Members

Name	Access	Summary
Dimension : Int32	public

Method Members

Name	Access	Summary
CalculateHessian() : GeneralMatrix	public	(from Net.Kniaz.Optimization.RealFunction)
GetDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetGradient() : Double[]	public	(from Net.Kniaz.Optimization.RealFunction)
GetHessian() : Double[][]	public	(from Net.Kniaz.Optimization.RealFunction)
GetPartialDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetVal() : Double	public

Parabola Class

Summary

public class Parabola : RealFunction, Net.Kniaz.Optimization.IGradientFunction, Net.Kniaz.Optimization.IFunction

Constructor Members

Name	Access	Summary
Parabola()	public	Initializes a new instance of the class.

Property Members

Name	Access	Summary
Dimension : Int32	public

Method Members

Name	Access	Summary
CalculateHessian() : GeneralMatrix	public	(from Net.Kniaz.Optimization.RealFunction)
GetDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetGradient() : Double[]	public	(from Net.Kniaz.Optimization.RealFunction)
GetHessian() : Double[][]	public	(from Net.Kniaz.Optimization.RealFunction)
GetPartialDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetVal() : Double	public

Banana Class

Summary

public class Banana : RealFunction, Net.Kniaz.Optimization.IGradientFunction, Net.Kniaz.Optimization.IFunction

Constructor Members

Name	Access	Summary
Banana()	public	Initializes a new instance of the class.

Property Members

Name	Access	Summary
Dimension : Int32	public

Method Members

Name	Access	Summary
CalculateHessian() : GeneralMatrix	public	(from Net.Kniaz.Optimization.RealFunction)
GetDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetGradient() : Double[]	public	(from Net.Kniaz.Optimization.RealFunction)
GetHessian() : Double[][]	public	(from Net.Kniaz.Optimization.RealFunction)
GetPartialDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetVal() : Double	public

Derivatives Class

Summary

public class Derivatives

Constructor Members

Name	Access	Summary
Derivatives()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
Hessian() : Void	public
PartialDerivative00() : Void	public
PartialDerivative01() : Void	public
PartialDerivative02() : Void	public
PartialDerivative10() : Void	public
PartialDerivative11() : Void	public
PartialDerivative12() : Void	public
PartialDerivative20() : Void	public
PartialDerivative21() : Void	public
PartialDerivative22() : Void	public

DFPTests Class

Summary

public class DFPTests

TestDFP.

Constructor Members

Name	Access	Summary
DFPTests()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
FitBFGS1() : Void	public
FitBFGS2() : Void	public
FitBFGS3() : Void	public
FitDFP1() : Void	public
FitDFP2() : Void	public
FitDFP3() : Void	public

GoldenTests Class

Summary

public class GoldenTests

Testing one dimensional minimum using the Golden Section Algorithm

Constructor Members

Name	Access	Summary
GoldenTests()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
MinGold1() : Void	public	Testing the algorithm using the test function test1 - a "w" shaped function Global Min is at x = -1.364641. We are starting with finding the bracket at 10 with step 1. Bracket function returns -4.764, -0.529, 6.326. These are fed to the 1D min function
MinGold2() : Void	public	This time the start ofsearch is close to the local minimum so the search should converge to local minimum
MinGold3() : Void	public	Tests regular parabola with a min of -0.75 coming from negative direction
MinGold4() : Void	public	testing a parabola coming from the far positive direction

IntervalTests Class

Summary

public class IntervalTests

Testing of the interval barcketing algorithm

Constructor Members

Name	Access	Summary
IntervalTests()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
MinInterval1() : Void	public	Try finding a bracket starting from negative end
MinInterval2() : Void	public	Start from the positive end
MinInterval3() : Void	public

Namespace : Net.Kniaz.Optimization.NonGradient

Net.Kniaz.Optimization.NonGradient Type List

Classes

Type	Summary
Nelder	Implements Nelder-Mead method of fiding minimum http://mathworld.wolfram.com/Nelder-MeadMethod.html
Rosenbrock	Implements the Rosenbrock optimization algorithm http://www.applied-mathematics.net/optimization/Rosenbrockbrock.html

Net.Kniaz.Optimization.NonGradient Classes

Nelder Class

Summary

public class Nelder

Implements Nelder-Mead method of fiding minimum http://mathworld.wolfram.com/Nelder-MeadMethod.html

Constructor Members

Name	Access	Summary
Nelder()	public	Parametrized constructor

Property Members

Name	Access	Summary
Epsilon : Double	public
Iterations : Int32	public
Itmax : Int32	public
Result : Double[]	public

Method Members

Name	Access	Summary
FindMinimum() : Void	public	Finds minimum for a function and parameters given in the constructor

Rosenbrock Class

Summary

public class Rosenbrock

Implements the Rosenbrock optimization algorithm http://www.applied-mathematics.net/optimization/Rosenbrockbrock.html

Constructor Members

Name	Access	Summary
Rosenbrock()	public	Parametrized constructor

Property Members

Name	Access	Summary
Epsilon : Double	public
Iterations : Int32	public
Itmax : Int32	public

Method Members

Name	Access	Summary
FindMinimum() : Void	public	Finds minimum of the function

Namespace : Net.Kniaz.Optimization.NonGradient.Tests

Net.Kniaz.Optimization.NonGradient.Tests Type List

Classes

Type	Summary
NelderTests	Tests Nelder Mead with 5 dimensional parabola and 3d Banana
RosenTests	Summary description for TestRosenbrock.

Net.Kniaz.Optimization.NonGradient.Tests Classes

NelderTests Class

Summary

public class NelderTests

Tests Nelder Mead with 5 dimensional parabola and 3d Banana

Constructor Members

Name	Access	Summary
NelderTests()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
CalculateBananaMinimum() : Void	public
CalculateParabolaMinimum() : Void	public

RosenTests Class

Summary

public class RosenTests

Summary description for TestRosenbrock.

Constructor Members

Name	Access	Summary
RosenTests()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
CalculateBananaMinimum() : Void	public	Calculate minimum of the rosebrock "Banana" function using Rosenbrock method
CalculateParabolaMinimum() : Void	public	Calculates the minimum of the 5 dimensional parabola using the rosenbrock Method

Namespace : Net.Kniaz.Optimization

Net.Kniaz.Optimization Type List

Interfaces

Type	Summary
IFunction	Interface for an arbitrary function of n dimensions
IGradientFunction	Interface for a Real function with gradient
IOneDFunction	Interface for real function of 1 dimension. Defined for use in linear searches.

Classes

Type	Summary
Banana	3 Dimensional banana - most gradient methods fail on this function. Rosenbrockbroock is very good at finding minimum for this
NumericNet	Helper function that calculates square root of sum of squares Used by the test function to test on minimum
Parabola	Summary description for Functions.
RealFunction	Summary description for RealFunction.
TestFunction	3 dimensional quadratic function with the minimum at (1,-2,3)
TestFunction1	Test function has a W like shape with the first dip being global minimum at x =~-1.5 and the second dip at x = 4
TestFunction2	A regular Parabola with a min of -0.75
TestFunction3	This function is "glued" from expotential and a parabola minimum is at 0.78152

Net.Kniaz.Optimization Interfaces

IFunction Interface

Summary

public interface IFunction

Interface for an arbitrary function of n dimensions

Property Members

Name	Access	Summary
Dimension : Int32	public	Returns dimension of the function

Method Members

Name	Access	Summary
GetVal() : Double	public	Return Value of the function for a value vector x

IGradientFunction Interface

Summary

public interface IGradientFunction : Net.Kniaz.Optimization.IFunction

Interface for a Real function with gradient

Method Members

Name	Access	Summary
GetDerivativeVal() : Double	public	returns the value of the derivative for the nth varaible at some point
GetGradient() : Double[]	public

IOneDFunction Interface

Summary

public interface IOneDFunction

Interface for real function of 1 dimension. Defined for use in linear searches.

Method Members

Name	Access	Summary
GetVal() : Double	public

Net.Kniaz.Optimization Classes

RealFunction Class

Summary

public abstract class RealFunction : Net.Kniaz.Optimization.IGradientFunction, Net.Kniaz.Optimization.IFunction

Summary description for RealFunction.

Constructor Members

Name	Access	Summary
RealFunction()	protected	Initializes a new instance of the class.

Property Members

Name	Access	Summary
Dimension : Int32	public

Method Members

Name	Access	Summary
CalculateHessian() : GeneralMatrix	public
GetDerivativeVal() : Double	public
GetGradient() : Double[]	public
GetHessian() : Double[][]	public
GetPartialDerivativeVal() : Double	public
GetVal() : Double	public

TestFunction Class

Summary

public class TestFunction : RealFunction, Net.Kniaz.Optimization.IGradientFunction, Net.Kniaz.Optimization.IFunction

3 dimensional quadratic function with the minimum at (1,-2,3)

Constructor Members

Name	Access	Summary
TestFunction()	public	Initializes a new instance of the class.

Property Members

Name	Access	Summary
Dimension : Int32	public

Method Members

Name	Access	Summary
CalculateHessian() : GeneralMatrix	public	(from Net.Kniaz.Optimization.RealFunction)
GetDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetGradient() : Double[]	public	(from Net.Kniaz.Optimization.RealFunction)
GetHessian() : Double[][]	public	(from Net.Kniaz.Optimization.RealFunction)
GetPartialDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetVal() : Double	public

TestFunction1 Class

Summary

public class TestFunction1 : Net.Kniaz.Optimization.IOneDFunction

Test function has a W like shape with the first dip being global minimum at x =~-1.5 and the second dip at x = 4

Constructor Members

Name	Access	Summary
TestFunction1()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
GetVal() : Double	public

TestFunction2 Class

Summary

public class TestFunction2 : Net.Kniaz.Optimization.IOneDFunction

A regular Parabola with a min of -0.75

Constructor Members

Name	Access	Summary
TestFunction2()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
GetVal() : Double	public

TestFunction3 Class

Summary

public class TestFunction3 : Net.Kniaz.Optimization.IOneDFunction

This function is "glued" from expotential and a parabola minimum is at 0.78152

Constructor Members

Name	Access	Summary
TestFunction3()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
GetVal() : Double	public

NumericNet Class

Summary

public class NumericNet

Helper function that calculates square root of sum of squares Used by the test function to test on minimum

Constructor Members

Name	Access	Summary
NumericNet()	public	Initializes a new instance of the class.

Method Members

Name	Access	Summary
CalcDiff() : Double	public

Parabola Class

Summary

public class Parabola : RealFunction, Net.Kniaz.Optimization.IGradientFunction, Net.Kniaz.Optimization.IFunction

Summary description for Functions.

Constructor Members

Name	Access	Summary
Parabola()	public

Property Members

Name	Access	Summary
Dimension : Int32	public

Method Members

Name	Access	Summary
CalculateHessian() : GeneralMatrix	public	(from Net.Kniaz.Optimization.RealFunction)
GetDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetGradient() : Double[]	public	(from Net.Kniaz.Optimization.RealFunction)
GetHessian() : Double[][]	public	(from Net.Kniaz.Optimization.RealFunction)
GetPartialDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetVal() : Double	public

Banana Class

Summary

public class Banana : RealFunction, Net.Kniaz.Optimization.IGradientFunction, Net.Kniaz.Optimization.IFunction

3 Dimensional banana - most gradient methods fail on this function. Rosenbrockbroock is very good at finding minimum for this

Constructor Members

Name	Access	Summary
Banana()	public	Initializes a new instance of the class.

Property Members

Name	Access	Summary
Dimension : Int32	public

Method Members

Name	Access	Summary
CalculateHessian() : GeneralMatrix	public	(from Net.Kniaz.Optimization.RealFunction)
GetDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetGradient() : Double[]	public	(from Net.Kniaz.Optimization.RealFunction)
GetHessian() : Double[][]	public	(from Net.Kniaz.Optimization.RealFunction)
GetPartialDerivativeVal() : Double	public	(from Net.Kniaz.Optimization.RealFunction)
GetVal() : Double	public