ITK  5.0.0
Insight Segmentation and Registration Toolkit
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itk::LBFGSOptimizer Class Reference

#include <itkLBFGSOptimizer.h>

+ Inheritance diagram for itk::LBFGSOptimizer:
+ Collaboration diagram for itk::LBFGSOptimizer:

Detailed Description

Wrap of the vnl_lbfgs algorithm for use in ITKv4 registration framework. The vnl_lbfgs is a wrapper for the NETLIB fortran code by Nocedal [1].

LBFGS is a quasi-Newton method. Quasi-Newton methods use an approximate estimate of the inverse Hessian $ (\nabla^2 f(x) )^{-1} $ to scale the gradient step:

\[ x_{n+1} = x_n - s (\nabla^2 f(x_n) )^{-1} \nabla f(x) \]

with $ s $ the step size.

The inverse Hessian is approximated from the gradients of previous iteration and thus only the gradient of the objective function is required.

The step size $ s $ is determined through line search with the approach by More and Thuente [4]. This line search approach finds a step size such that

\[ \lVert \nabla f(x + s (\nabla^2 f(x_n) )^{-1} \nabla f(x) ) \rVert \le \nu \lVert \nabla f(x) \rVert \]

The parameter $ \nu $ is set through SetLineSearchAccuracy() (default 0.9) The default step length, i.e. starting step length for the line search, is set through SetDefaultStepLength() (default 1.0).

The optimization stops when either the gradient satisfies the condition

\[ \lVert \nabla f(x) \rVert \le \epsilon \max(1, \lVert X \rVert) \]

or a maximum number of function evaluations has been reached. The tolerance $\epsilon$ is set through SetGradientConvergenceTolerance() (default 1e-5) and the maximum number of function evaluations is set through SetMaximumNumberOfFunctionEvaluations() (default 2000).

Note: The scales set through SetScales should be set or left at one. Otherwise the Hessian approximation will be disturbed and the optimizer is unlikely to find a minima.


[1] NETLIB lbfgs

[2] Jorge Nocedal. Updating Quasi-Newton Matrices with Limited Storage. Mathematics of Computation, Vol. 35, No. 151, pp. 773-782, 1980.

[3] Dong C. Liu and Jorge Nocedal. On the limited memory BFGS method for large scale optimization. Mathematical Programming B, Vol. 45, No. 3, pp. 503-528, 1989.

[4] More, J. J. and D. J. Thuente. Line Search Algorithms with Guaranteed Sufficient Decrease. ACM Transactions on Mathematical Software 20, no. 3 (1994): 286-307.

Examples/RegistrationITKv3/DeformableRegistration4.cxx, Examples/RegistrationITKv3/DeformableRegistration6.cxx, and WikiExamples/Registration/ImageRegistrationMethodBSpline.cxx.

Definition at line 85 of file itkLBFGSOptimizer.h.

Public Types

using ConstPointer = SmartPointer< const Self >
using InternalOptimizerType = vnl_lbfgs
using InternalParametersType = vnl_vector< double >
using Pointer = SmartPointer< Self >
using Self = LBFGSOptimizer
using Superclass = SingleValuedNonLinearVnlOptimizer
- Public Types inherited from itk::SingleValuedNonLinearVnlOptimizer
using CommandType = ReceptorMemberCommand< Self >
using ConstPointer = SmartPointer< const Self >
using Pointer = SmartPointer< Self >
using Self = SingleValuedNonLinearVnlOptimizer
using Superclass = SingleValuedNonLinearOptimizer
- Public Types inherited from itk::SingleValuedNonLinearOptimizer
using ConstPointer = SmartPointer< const Self >
using CostFunctionPointer = CostFunctionType::Pointer
using CostFunctionType = SingleValuedCostFunction
using DerivativeType = CostFunctionType::DerivativeType
using MeasureType = CostFunctionType::MeasureType
using ParametersType = Superclass::ParametersType
using Pointer = SmartPointer< Self >
using Self = SingleValuedNonLinearOptimizer
using Superclass = NonLinearOptimizer
- Public Types inherited from itk::NonLinearOptimizer
using ConstPointer = SmartPointer< const Self >
using ParametersType = Superclass::ParametersType
using Pointer = SmartPointer< Self >
using ScalesType = Superclass::ScalesType
using Self = NonLinearOptimizer
using Superclass = Optimizer
- Public Types inherited from itk::Optimizer
using ConstPointer = SmartPointer< const Self >
using ParametersType = OptimizerParameters< double >
using Pointer = SmartPointer< Self >
using ScalesType = Array< double >
using Self = Optimizer
using Superclass = Object
- Public Types inherited from itk::Object
using ConstPointer = SmartPointer< const Self >
using Pointer = SmartPointer< Self >
using Self = Object
using Superclass = LightObject
- Public Types inherited from itk::LightObject
using ConstPointer = SmartPointer< const Self >
using Pointer = SmartPointer< Self >
using Self = LightObject

Public Member Functions

virtual ::itk::LightObject::Pointer CreateAnother () const
virtual double GetDefaultStepLength ()
virtual double GetGradientConvergenceTolerance ()
virtual double GetLineSearchAccuracy ()
virtual unsigned int GetMaximumNumberOfFunctionEvaluations ()
virtual const char * GetNameOfClass () const
vnl_lbfgs * GetOptimizer ()
const std::string GetStopConditionDescription () const override
virtual bool GetTrace ()
MeasureType GetValue () const
void SetCostFunction (SingleValuedCostFunction *costFunction) override
virtual void SetDefaultStepLength (double stp)
virtual void SetGradientConvergenceTolerance (double gtol)
virtual void SetLineSearchAccuracy (double tol)
virtual void SetMaximumNumberOfFunctionEvaluations (unsigned int n)
virtual void SetTrace (bool flag)
void StartOptimization () override
virtual void TraceOff ()
virtual void TraceOn ()
- Public Member Functions inherited from itk::SingleValuedNonLinearVnlOptimizer
virtual const bool & GetMaximize () const
virtual void SetMaximize (bool _arg)
virtual void MaximizeOn ()
virtual void MaximizeOff ()
bool GetMinimize () const
void SetMinimize (bool v)
void MinimizeOn ()
void MinimizeOff ()
virtual const MeasureTypeGetCachedValue () const
virtual const DerivativeTypeGetCachedDerivative () const
virtual const ParametersTypeGetCachedCurrentPosition () const
- Public Member Functions inherited from itk::SingleValuedNonLinearOptimizer
virtual ::itk::LightObject::Pointer CreateAnother () const
virtual const CostFunctionTypeGetCostFunction () const
virtual CostFunctionTypeGetModifiableCostFunction ()
MeasureType GetValue (const ParametersType &parameters) const
virtual void SetCostFunction (CostFunctionType *costFunction)
- Public Member Functions inherited from itk::Optimizer
virtual const ParametersTypeGetCurrentPosition () const
virtual const ParametersTypeGetInitialPosition () const
virtual void SetInitialPosition (const ParametersType &param)
void SetScales (const ScalesType &scales)
virtual const ScalesTypeGetScales () const
virtual const ScalesTypeGetInverseScales () const
- Public Member Functions inherited from itk::Object
unsigned long AddObserver (const EventObject &event, Command *)
unsigned long AddObserver (const EventObject &event, Command *) const
virtual void DebugOff () const
virtual void DebugOn () const
CommandGetCommand (unsigned long tag)
bool GetDebug () const
MetaDataDictionaryGetMetaDataDictionary ()
const MetaDataDictionaryGetMetaDataDictionary () const
virtual ModifiedTimeType GetMTime () const
virtual const TimeStampGetTimeStamp () const
bool HasObserver (const EventObject &event) const
void InvokeEvent (const EventObject &)
void InvokeEvent (const EventObject &) const
virtual void Modified () const
void Register () const override
void RemoveAllObservers ()
void RemoveObserver (unsigned long tag)
void SetDebug (bool debugFlag) const
void SetReferenceCount (int) override
void UnRegister () const noexceptoverride
void SetMetaDataDictionary (const MetaDataDictionary &rhs)
void SetMetaDataDictionary (MetaDataDictionary &&rrhs)
virtual void SetObjectName (std::string _arg)
virtual const std::string & GetObjectName () const
- Public Member Functions inherited from itk::LightObject
virtual void Delete ()
virtual int GetReferenceCount () const
 itkCloneMacro (Self)
void Print (std::ostream &os, Indent indent=0) const

Static Public Member Functions

static Pointer New ()
- Static Public Member Functions inherited from itk::SingleValuedNonLinearOptimizer
static Pointer New ()
- Static Public Member Functions inherited from itk::NonLinearOptimizer
static Pointer New ()
- Static Public Member Functions inherited from itk::Optimizer
static Pointer New ()
- Static Public Member Functions inherited from itk::Object
static bool GetGlobalWarningDisplay ()
static void GlobalWarningDisplayOff ()
static void GlobalWarningDisplayOn ()
static Pointer New ()
static void SetGlobalWarningDisplay (bool flag)
- Static Public Member Functions inherited from itk::LightObject
static void BreakOnError ()
static Pointer New ()

Protected Types

using CostFunctionAdaptorType = Superclass::CostFunctionAdaptorType
- Protected Types inherited from itk::SingleValuedNonLinearVnlOptimizer
using CostFunctionAdaptorType = SingleValuedVnlCostFunctionAdaptor

Protected Member Functions

 LBFGSOptimizer ()
void PrintSelf (std::ostream &os, Indent indent) const override
 ~LBFGSOptimizer () override
- Protected Member Functions inherited from itk::SingleValuedNonLinearVnlOptimizer
const CostFunctionAdaptorTypeGetCostFunctionAdaptor () const
CostFunctionAdaptorTypeGetCostFunctionAdaptor ()
CostFunctionAdaptorTypeGetNonConstCostFunctionAdaptor () const
void PrintSelf (std::ostream &os, Indent indent) const override
void SetCostFunctionAdaptor (CostFunctionAdaptorType *adaptor)
 SingleValuedNonLinearVnlOptimizer ()
 ~SingleValuedNonLinearVnlOptimizer () override
- Protected Member Functions inherited from itk::SingleValuedNonLinearOptimizer
 SingleValuedNonLinearOptimizer ()
 ~SingleValuedNonLinearOptimizer () override=default
- Protected Member Functions inherited from itk::NonLinearOptimizer
 NonLinearOptimizer ()=default
 ~NonLinearOptimizer () override
- Protected Member Functions inherited from itk::Optimizer
 Optimizer ()
virtual void SetCurrentPosition (const ParametersType &param)
 ~Optimizer () override=default
- Protected Member Functions inherited from itk::Object
 Object ()
bool PrintObservers (std::ostream &os, Indent indent) const
virtual void SetTimeStamp (const TimeStamp &time)
 ~Object () override
- Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer InternalClone () const
 LightObject ()
virtual void PrintHeader (std::ostream &os, Indent indent) const
virtual void PrintTrailer (std::ostream &os, Indent indent) const
virtual ~LightObject ()

Private Attributes

double m_DefaultStepLength
double m_GradientConvergenceTolerance
double m_LineSearchAccuracy
unsigned int m_MaximumNumberOfFunctionEvaluations
bool m_OptimizerInitialized
std::ostringstream m_StopConditionDescription
bool m_Trace

Additional Inherited Members

- Protected Attributes inherited from itk::SingleValuedNonLinearOptimizer
CostFunctionPointer m_CostFunction
- Protected Attributes inherited from itk::Optimizer
ParametersType m_CurrentPosition
bool m_ScalesInitialized { false }
- Protected Attributes inherited from itk::LightObject
std::atomic< int > m_ReferenceCount

Member Typedef Documentation

Definition at line 95 of file itkLBFGSOptimizer.h.

using itk::LBFGSOptimizer::CostFunctionAdaptorType = Superclass::CostFunctionAdaptorType

Definition at line 169 of file itkLBFGSOptimizer.h.

Internal optimizer type.

Definition at line 107 of file itkLBFGSOptimizer.h.

using itk::LBFGSOptimizer::InternalParametersType = vnl_vector< double >

InternalParameters type alias.

Definition at line 104 of file itkLBFGSOptimizer.h.

Definition at line 94 of file itkLBFGSOptimizer.h.

Standard "Self" type alias.

Definition at line 92 of file itkLBFGSOptimizer.h.

Definition at line 93 of file itkLBFGSOptimizer.h.

Constructor & Destructor Documentation

itk::LBFGSOptimizer::LBFGSOptimizer ( )
itk::LBFGSOptimizer::~LBFGSOptimizer ( )

Member Function Documentation

virtual::itk::LightObject::Pointer itk::LBFGSOptimizer::CreateAnother ( ) const

Create an object from an instance, potentially deferring to a factory. This method allows you to create an instance of an object that is exactly the same type as the referring object. This is useful in cases where an object has been cast back to a base class.

Reimplemented from itk::Object.

virtual double itk::LBFGSOptimizer::GetDefaultStepLength ( )
virtual double itk::LBFGSOptimizer::GetGradientConvergenceTolerance ( )
virtual double itk::LBFGSOptimizer::GetLineSearchAccuracy ( )
virtual unsigned int itk::LBFGSOptimizer::GetMaximumNumberOfFunctionEvaluations ( )
virtual const char* itk::LBFGSOptimizer::GetNameOfClass ( ) const

Run-time type information (and related methods).

Reimplemented from itk::SingleValuedNonLinearVnlOptimizer.

vnl_lbfgs* itk::LBFGSOptimizer::GetOptimizer ( )

Method for getting access to the internal optimizer.

const std::string itk::LBFGSOptimizer::GetStopConditionDescription ( ) const

Get the reason for termination

Reimplemented from itk::Optimizer.

virtual bool itk::LBFGSOptimizer::GetTrace ( )
MeasureType itk::LBFGSOptimizer::GetValue ( ) const

Return Current Value

static Pointer itk::LBFGSOptimizer::New ( )

Method for creation through the object factory.

void itk::LBFGSOptimizer::PrintSelf ( std::ostream &  os,
Indent  indent 
) const

Methods invoked by Print() to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from itk::Object.

void itk::LBFGSOptimizer::SetCostFunction ( SingleValuedCostFunction costFunction)

Plug in a Cost Function into the optimizer

Implements itk::SingleValuedNonLinearVnlOptimizer.

virtual void itk::LBFGSOptimizer::SetDefaultStepLength ( double  stp)

Set/Get the default step size. This is a positive real number with a default value of 1.0 which determines the stpe size in the line search.

virtual void itk::LBFGSOptimizer::SetGradientConvergenceTolerance ( double  gtol)

Set/Get the gradient convergence tolerance. This is a positive real number that determines the accuracy with which the solution is to be found. The optimization terminates when: ||G|| < gtol max(1,||X||) where ||.|| denotes the Euclidean norm.

virtual void itk::LBFGSOptimizer::SetLineSearchAccuracy ( double  tol)

Set/Get the line search accuracy. This is a positive real number with a default value of 0.9, which controls the accuracy of the line search. If the function and gradient evalutions are inexpensive with respect to the cost of the iterations it may be advantageous to set the value to a small value (say 0.1).

virtual void itk::LBFGSOptimizer::SetMaximumNumberOfFunctionEvaluations ( unsigned int  n)

Set/Get the maximum number of function evaluations allowed.

virtual void itk::LBFGSOptimizer::SetTrace ( bool  flag)

Set/Get the optimizer trace flag. If set to true, the optimizer prints out information every iteration.

void itk::LBFGSOptimizer::StartOptimization ( )

Start optimization with an initial value.

Reimplemented from itk::Optimizer.

virtual void itk::LBFGSOptimizer::TraceOff ( )
virtual void itk::LBFGSOptimizer::TraceOn ( )

Member Data Documentation

double itk::LBFGSOptimizer::m_DefaultStepLength

Definition at line 180 of file itkLBFGSOptimizer.h.

double itk::LBFGSOptimizer::m_GradientConvergenceTolerance

Definition at line 178 of file itkLBFGSOptimizer.h.

double itk::LBFGSOptimizer::m_LineSearchAccuracy

Definition at line 179 of file itkLBFGSOptimizer.h.

unsigned int itk::LBFGSOptimizer::m_MaximumNumberOfFunctionEvaluations

Definition at line 177 of file itkLBFGSOptimizer.h.

bool itk::LBFGSOptimizer::m_OptimizerInitialized

Definition at line 172 of file itkLBFGSOptimizer.h.

std::ostringstream itk::LBFGSOptimizer::m_StopConditionDescription

Definition at line 174 of file itkLBFGSOptimizer.h.

bool itk::LBFGSOptimizer::m_Trace

Definition at line 176 of file itkLBFGSOptimizer.h.

InternalOptimizerType* itk::LBFGSOptimizer::m_VnlOptimizer

Definition at line 173 of file itkLBFGSOptimizer.h.

The documentation for this class was generated from the following file: