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itk::QuasiNewtonLBFGSOptimizer Class Reference
Components » Optimizers

#include <itkQuasiNewtonLBFGSOptimizer.h>

Detailed Description

ITK version of the lbfgs algorithm ...

This class is an ITK version of the netlib lbfgs_ function. It gives exactly the same results, if used in combination with the itk::MoreThuenteLineSearchOptimizer.

The optimizer solves the unconstrained minimization problem

\[ \min F(x), \quad x = ( x_1,x_2,\ldots,x_N ), \]

using the limited memory BFGS method. The routine is especially effective on problems involving a large number of variables. In a typical iteration of this method an approximation $H_k$ to the inverse of the Hessian is obtained by applying $M$ BFGS updates to a diagonal matrix $H_0$, using information from the previous $M$ steps. The user specifies the number $M$ (Memory), which determines the amount of storage required by the routine.

The algorithm is described in "On the limited memory BFGS method for large scale optimization", by D. Liu and J. Nocedal, Mathematical Programming B 45 (1989) 503-528.

The steplength is determined at each iteration by means of a line search routine. The itk::MoreThuenteLineSearchOptimizer works well.

Definition at line 58 of file itkQuasiNewtonLBFGSOptimizer.h.

Inheritance diagram for itk::QuasiNewtonLBFGSOptimizer:
Inheritance graph
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Public Types

using ConstPointer = SmartPointer<const Self>
 
using DiagonalMatrixType = Array<double>
 
using LineSearchOptimizerPointer = LineSearchOptimizerType::Pointer
 
using LineSearchOptimizerType = LineSearchOptimizer
 
using Pointer = SmartPointer<Self>
 
using RhoType = Array<double>
 
using ScaledCostFunctionType
 
using ScalesType
 
using Self = QuasiNewtonLBFGSOptimizer
 
enum class  StopConditionType {
  MetricError , LineSearchError , MaximumNumberOfIterations , InvalidDiagonalMatrix ,
  GradientMagnitudeTolerance , ZeroStep , Unknown
}
 
using SType = std::vector<ParametersType>
 
using Superclass = ScaledSingleValuedNonLinearOptimizer
 
using YType = std::vector<DerivativeType>
 
- Public Types inherited from itk::ScaledSingleValuedNonLinearOptimizer
using ConstPointer = SmartPointer<const Self>
 
using Pointer = SmartPointer<Self>
 
using ScaledCostFunctionPointer = ScaledCostFunctionType::Pointer
 
using ScaledCostFunctionType = ScaledSingleValuedCostFunction
 
using ScalesType = NonLinearOptimizer::ScalesType
 
using Self = ScaledSingleValuedNonLinearOptimizer
 
using Superclass = SingleValuedNonLinearOptimizer
 

Public Member Functions

virtual const char * GetClassName () const
 
virtual const DerivativeType & GetCurrentGradient ()
 
virtual unsigned long GetCurrentIteration () const
 
virtual double GetCurrentStepLength () const
 
virtual MeasureType GetCurrentValue () const
 
virtual double GetGradientMagnitudeTolerance () const
 
virtual bool GetInLineSearch () const
 
virtual unsigned long GetMaximumNumberOfIterations () const
 
virtual unsigned int GetMemory () const
 
virtual const StopConditionType & GetStopCondition ()
 
 ITK_DISALLOW_COPY_AND_MOVE (QuasiNewtonLBFGSOptimizer)
 
 itkGetModifiableObjectMacro (LineSearchOptimizer, LineSearchOptimizerType)
 
virtual void ResumeOptimization ()
 
virtual void SetGradientMagnitudeTolerance (double _arg)
 
virtual void SetLineSearchOptimizer (LineSearchOptimizerType *_arg)
 
virtual void SetMaximumNumberOfIterations (unsigned long _arg)
 
virtual void SetMemory (unsigned int _arg)
 
void StartOptimization () override
 
virtual void StopOptimization ()
 
- Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
const ParametersType & GetCurrentPosition () const override
 
virtual bool GetMaximize () const
 
virtual const ScaledCostFunctionType * GetScaledCostFunction ()
 
virtual const ParametersType & GetScaledCurrentPosition ()
 
bool GetUseScales () const
 
virtual void InitializeScales ()
 
 ITK_DISALLOW_COPY_AND_MOVE (ScaledSingleValuedNonLinearOptimizer)
 
virtual void MaximizeOff ()
 
virtual void MaximizeOn ()
 
void SetCostFunction (CostFunctionType *costFunction) override
 
virtual void SetMaximize (bool _arg)
 
virtual void SetUseScales (bool arg)
 

Static Public Member Functions

static Pointer New ()
 
- Static Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
static Pointer New ()
 

Protected Member Functions

virtual void ComputeDiagonalMatrix (DiagonalMatrixType &diag_H0)
 
virtual void ComputeSearchDirection (const DerivativeType &gradient, ParametersType &searchDir)
 
virtual void LineSearch (const ParametersType searchDir, double &step, ParametersType &x, MeasureType &f, DerivativeType &g)
 
void PrintSelf (std::ostream &, Indent) const override
 
 QuasiNewtonLBFGSOptimizer ()
 
virtual void SetInLineSearch (bool _arg)
 
virtual void StoreCurrentPoint (const ParametersType &step, const DerivativeType &grad_dif)
 
virtual bool TestConvergence (bool firstLineSearchDone)
 
 ~QuasiNewtonLBFGSOptimizer () override=default
 
- Protected Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual void GetScaledDerivative (const ParametersType &parameters, DerivativeType &derivative) const
 
virtual MeasureType GetScaledValue (const ParametersType &parameters) const
 
virtual void GetScaledValueAndDerivative (const ParametersType &parameters, MeasureType &value, DerivativeType &derivative) const
 
void PrintSelf (std::ostream &os, Indent indent) const override
 
 ScaledSingleValuedNonLinearOptimizer ()
 
void SetCurrentPosition (const ParametersType &param) override
 
virtual void SetScaledCurrentPosition (const ParametersType &parameters)
 
 ~ScaledSingleValuedNonLinearOptimizer () override=default
 

Protected Attributes

unsigned int m_Bound { 0 }
 
DerivativeType m_CurrentGradient {}
 
unsigned long m_CurrentIteration { 0 }
 
double m_CurrentStepLength { 0.0 }
 
MeasureType m_CurrentValue { 0.0 }
 
bool m_InLineSearch { false }
 
unsigned int m_Point { 0 }
 
unsigned int m_PreviousPoint { 0 }
 
RhoType m_Rho {}
 
SType m_S {}
 
bool m_Stop { false }
 
StopConditionType m_StopCondition { StopConditionType::Unknown }
 
YType m_Y {}
 
- Protected Attributes inherited from itk::ScaledSingleValuedNonLinearOptimizer
ScaledCostFunctionPointer m_ScaledCostFunction {}
 
ParametersType m_ScaledCurrentPosition {}
 

Private Attributes

double m_GradientMagnitudeTolerance { 1e-5 }
 
LineSearchOptimizerPointer m_LineSearchOptimizer { nullptr }
 
unsigned long m_MaximumNumberOfIterations { 100 }
 
unsigned int m_Memory { 5 }
 

Member Typedef Documentation

◆ ConstPointer

using itk::QuasiNewtonLBFGSOptimizer::ConstPointer = SmartPointer<const Self>

Definition at line 66 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ DiagonalMatrixType

using itk::QuasiNewtonLBFGSOptimizer::DiagonalMatrixType = Array<double>

Definition at line 81 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ LineSearchOptimizerPointer

using itk::QuasiNewtonLBFGSOptimizer::LineSearchOptimizerPointer = LineSearchOptimizerType::Pointer

Definition at line 84 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ LineSearchOptimizerType

using itk::QuasiNewtonLBFGSOptimizer::LineSearchOptimizerType = LineSearchOptimizer

Definition at line 82 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ Pointer

using itk::QuasiNewtonLBFGSOptimizer::Pointer = SmartPointer<Self>

Definition at line 65 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ RhoType

using itk::QuasiNewtonLBFGSOptimizer::RhoType = Array<double>

Definition at line 78 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ ScaledCostFunctionType

using itk::ScaledSingleValuedNonLinearOptimizer::ScaledCostFunctionType

Definition at line 86 of file itkScaledSingleValuedNonLinearOptimizer.h.

◆ ScalesType

using itk::ScaledSingleValuedNonLinearOptimizer::ScalesType

Definition at line 85 of file itkScaledSingleValuedNonLinearOptimizer.h.

◆ Self

using itk::QuasiNewtonLBFGSOptimizer::Self = QuasiNewtonLBFGSOptimizer

Definition at line 63 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ SType

using itk::QuasiNewtonLBFGSOptimizer::SType = std::vector<ParametersType>

Definition at line 79 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ Superclass

using itk::QuasiNewtonLBFGSOptimizer::Superclass = ScaledSingleValuedNonLinearOptimizer

Definition at line 64 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ YType

using itk::QuasiNewtonLBFGSOptimizer::YType = std::vector<DerivativeType>

Definition at line 80 of file itkQuasiNewtonLBFGSOptimizer.h.

Member Enumeration Documentation

◆ StopConditionType

enum class itk::QuasiNewtonLBFGSOptimizer::StopConditionType
strong
Enumerator
MetricError 
LineSearchError 
MaximumNumberOfIterations 
InvalidDiagonalMatrix 
GradientMagnitudeTolerance 
ZeroStep 
Unknown 

Definition at line 86 of file itkQuasiNewtonLBFGSOptimizer.h.

Constructor & Destructor Documentation

◆ QuasiNewtonLBFGSOptimizer()

itk::QuasiNewtonLBFGSOptimizer::QuasiNewtonLBFGSOptimizer ( )
protected

◆ ~QuasiNewtonLBFGSOptimizer()

itk::QuasiNewtonLBFGSOptimizer::~QuasiNewtonLBFGSOptimizer ( )
overrideprotecteddefault

Member Function Documentation

◆ ComputeDiagonalMatrix()

virtual void itk::QuasiNewtonLBFGSOptimizer::ComputeDiagonalMatrix ( DiagonalMatrixType & diag_H0)
protectedvirtual

Compute H0

Override this method if not satisfied with the default choice.

◆ ComputeSearchDirection()

virtual void itk::QuasiNewtonLBFGSOptimizer::ComputeSearchDirection ( const DerivativeType & gradient,
ParametersType & searchDir )
protectedvirtual

Compute -Hg

COMPUTE -H*G USING THE FORMULA GIVEN IN: Nocedal, J. 1980, "Updating quasi-Newton matrices with limited storage", Mathematics of Computation, Vol.24, No.151, pp. 773-782.

◆ GetClassName()

virtual const char * itk::QuasiNewtonLBFGSOptimizer::GetClassName ( ) const
virtual

Reimplemented from itk::ScaledSingleValuedNonLinearOptimizer.

Reimplemented in elastix::QuasiNewtonLBFGS< TElastix >.

◆ GetCurrentGradient()

virtual const DerivativeType & itk::QuasiNewtonLBFGSOptimizer::GetCurrentGradient ( )
virtual

◆ GetCurrentIteration()

virtual unsigned long itk::QuasiNewtonLBFGSOptimizer::GetCurrentIteration ( ) const
virtual

Get information about optimization process:

◆ GetCurrentStepLength()

virtual double itk::QuasiNewtonLBFGSOptimizer::GetCurrentStepLength ( ) const
virtual

◆ GetCurrentValue()

virtual MeasureType itk::QuasiNewtonLBFGSOptimizer::GetCurrentValue ( ) const
virtual

◆ GetGradientMagnitudeTolerance()

virtual double itk::QuasiNewtonLBFGSOptimizer::GetGradientMagnitudeTolerance ( ) const
virtual

Setting: the mininum gradient magnitude.

The optimizer stops when: ||CurrentGradient|| < GradientMagnitudeTolerance * max(1, ||CurrentPosition||)

◆ GetInLineSearch()

virtual bool itk::QuasiNewtonLBFGSOptimizer::GetInLineSearch ( ) const
virtual

◆ GetMaximumNumberOfIterations()

virtual unsigned long itk::QuasiNewtonLBFGSOptimizer::GetMaximumNumberOfIterations ( ) const
virtual

Setting: the maximum number of iterations

◆ GetMemory()

virtual unsigned int itk::QuasiNewtonLBFGSOptimizer::GetMemory ( ) const
virtual

◆ GetStopCondition()

virtual const StopConditionType & itk::QuasiNewtonLBFGSOptimizer::GetStopCondition ( )
virtual

◆ ITK_DISALLOW_COPY_AND_MOVE()

itk::QuasiNewtonLBFGSOptimizer::ITK_DISALLOW_COPY_AND_MOVE ( QuasiNewtonLBFGSOptimizer )

◆ itkGetModifiableObjectMacro()

itk::QuasiNewtonLBFGSOptimizer::itkGetModifiableObjectMacro ( LineSearchOptimizer ,
LineSearchOptimizerType  )

◆ LineSearch()

virtual void itk::QuasiNewtonLBFGSOptimizer::LineSearch ( const ParametersType searchDir,
double & step,
ParametersType & x,
MeasureType & f,
DerivativeType & g )
protectedvirtual

Perform a line search along the search direction. On calling, x, f, and g should contain the current position, the cost function value at this position, and the derivative. On return the step, x (new position), f (value at x), and g (derivative at x) are updated.

◆ New()

static Pointer itk::QuasiNewtonLBFGSOptimizer::New ( )
static

◆ PrintSelf()

void itk::QuasiNewtonLBFGSOptimizer::PrintSelf ( std::ostream & ,
Indent  ) const
inlineoverrideprotected

Definition at line 142 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ ResumeOptimization()

virtual void itk::QuasiNewtonLBFGSOptimizer::ResumeOptimization ( )
virtual

◆ SetGradientMagnitudeTolerance()

virtual void itk::QuasiNewtonLBFGSOptimizer::SetGradientMagnitudeTolerance ( double _arg)
virtual

◆ SetInLineSearch()

virtual void itk::QuasiNewtonLBFGSOptimizer::SetInLineSearch ( bool _arg)
protectedvirtual

◆ SetLineSearchOptimizer()

virtual void itk::QuasiNewtonLBFGSOptimizer::SetLineSearchOptimizer ( LineSearchOptimizerType * _arg)
virtual

Setting: the line search optimizer

◆ SetMaximumNumberOfIterations()

virtual void itk::QuasiNewtonLBFGSOptimizer::SetMaximumNumberOfIterations ( unsigned long _arg)
virtual

◆ SetMemory()

virtual void itk::QuasiNewtonLBFGSOptimizer::SetMemory ( unsigned int _arg)
virtual

Setting: the memory. The number of iterations that are used to estimate the Hessian. 5 by default. 0 results in (normalised) gradient descent search directions

◆ StartOptimization()

void itk::QuasiNewtonLBFGSOptimizer::StartOptimization ( )
override

◆ StopOptimization()

virtual void itk::QuasiNewtonLBFGSOptimizer::StopOptimization ( )
virtual

◆ StoreCurrentPoint()

virtual void itk::QuasiNewtonLBFGSOptimizer::StoreCurrentPoint ( const ParametersType & step,
const DerivativeType & grad_dif )
protectedvirtual

Store s = x_k - x_k-1 and y = g_k - g_k-1 in m_S and m_Y, and store 1/(ys) in m_Rho.

◆ TestConvergence()

virtual bool itk::QuasiNewtonLBFGSOptimizer::TestConvergence ( bool firstLineSearchDone)
protectedvirtual

Check if convergence has occurred; The firstLineSearchDone bool allows the implementation of TestConvergence to decide to skip a few convergence checks when no line search has performed yet (so, before the actual optimisation begins)

Reimplemented in elastix::QuasiNewtonLBFGS< TElastix >.

Field Documentation

◆ m_Bound

unsigned int itk::QuasiNewtonLBFGSOptimizer::m_Bound { 0 }
protected

Definition at line 161 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_CurrentGradient

DerivativeType itk::QuasiNewtonLBFGSOptimizer::m_CurrentGradient {}
protected

Definition at line 145 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_CurrentIteration

unsigned long itk::QuasiNewtonLBFGSOptimizer::m_CurrentIteration { 0 }
protected

Definition at line 147 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_CurrentStepLength

double itk::QuasiNewtonLBFGSOptimizer::m_CurrentStepLength { 0.0 }
protected

Definition at line 150 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_CurrentValue

MeasureType itk::QuasiNewtonLBFGSOptimizer::m_CurrentValue { 0.0 }
protected

Definition at line 146 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_GradientMagnitudeTolerance

double itk::QuasiNewtonLBFGSOptimizer::m_GradientMagnitudeTolerance { 1e-5 }
private

Definition at line 202 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_InLineSearch

bool itk::QuasiNewtonLBFGSOptimizer::m_InLineSearch { false }
protected

Is true when the LineSearchOptimizer has been started.

Definition at line 153 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_LineSearchOptimizer

LineSearchOptimizerPointer itk::QuasiNewtonLBFGSOptimizer::m_LineSearchOptimizer { nullptr }
private

Definition at line 203 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_MaximumNumberOfIterations

unsigned long itk::QuasiNewtonLBFGSOptimizer::m_MaximumNumberOfIterations { 100 }
private

Definition at line 201 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_Memory

unsigned int itk::QuasiNewtonLBFGSOptimizer::m_Memory { 5 }
private

Definition at line 204 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_Point

unsigned int itk::QuasiNewtonLBFGSOptimizer::m_Point { 0 }
protected

Definition at line 159 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_PreviousPoint

unsigned int itk::QuasiNewtonLBFGSOptimizer::m_PreviousPoint { 0 }
protected

Definition at line 160 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_Rho

RhoType itk::QuasiNewtonLBFGSOptimizer::m_Rho {}
protected

Definition at line 155 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_S

SType itk::QuasiNewtonLBFGSOptimizer::m_S {}
protected

Definition at line 156 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_Stop

bool itk::QuasiNewtonLBFGSOptimizer::m_Stop { false }
protected

Definition at line 149 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_StopCondition

StopConditionType itk::QuasiNewtonLBFGSOptimizer::m_StopCondition { StopConditionType::Unknown }
protected

Definition at line 148 of file itkQuasiNewtonLBFGSOptimizer.h.

◆ m_Y

YType itk::QuasiNewtonLBFGSOptimizer::m_Y {}
protected

Definition at line 157 of file itkQuasiNewtonLBFGSOptimizer.h.


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