ITK  4.13.0
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itk::LBFGSOptimizer Class Reference
Numerics | Optimizers | Module ITKOptimizers

#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.

References:

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

Definition at line 85 of file itkLBFGSOptimizer.h.

Public Types

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

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 ()
 
virtual const std::string GetStopConditionDescription () const override
 
virtual bool GetTrace ()
 
MeasureType GetValue () const
 
virtual 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)
 
virtual void StartOptimization (void) 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 MeasureType & GetCachedValue () const
 
virtual const DerivativeType & GetCachedDerivative () const
 
virtual const ParametersType & GetCachedCurrentPosition () const
 
- Public Member Functions inherited from itk::SingleValuedNonLinearOptimizer
virtual ::itk::LightObject::Pointer CreateAnother () const
 
virtual const CostFunctionType * GetCostFunction () const
 
virtual CostFunctionType * GetModifiableCostFunction ()
 
MeasureType GetValue (const ParametersType &parameters) const
 
virtual void SetCostFunction (CostFunctionType *costFunction)
 
- Public Member Functions inherited from itk::Optimizer
virtual const ParametersType & GetCurrentPosition () const
 
virtual const ParametersType & GetInitialPosition () const
 
virtual void SetInitialPosition (const ParametersType &param)
 
void SetScales (const ScalesType &scales)
 
virtual const ScalesType & GetScales () const
 
virtual const ScalesType & GetInverseScales () 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
 
Command * GetCommand (unsigned long tag)
 
bool GetDebug () const
 
MetaDataDictionary & GetMetaDataDictionary ()
 
const MetaDataDictionary & GetMetaDataDictionary () const
 
virtual ModifiedTimeType GetMTime () const
 
virtual const TimeStamp & GetTimeStamp () const
 
bool HasObserver (const EventObject &event) const
 
void InvokeEvent (const EventObject &)
 
void InvokeEvent (const EventObject &) const
 
virtual void Modified () const
 
virtual void Register () const override
 
void RemoveAllObservers ()
 
void RemoveObserver (unsigned long tag)
 
void SetDebug (bool debugFlag) const
 
void SetMetaDataDictionary (const MetaDataDictionary &rhs)
 
virtual void SetReferenceCount (int) override
 
virtual void UnRegister () const noexceptoverride
 
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

typedef
Superclass::CostFunctionAdaptorType 		CostFunctionAdaptorType
 
- Protected Types inherited from itk::SingleValuedNonLinearVnlOptimizer
typedef
SingleValuedVnlCostFunctionAdaptor 		CostFunctionAdaptorType
 

Protected Member Functions

 LBFGSOptimizer ()
 
virtual void PrintSelf (std::ostream &os, Indent indent) const override
 
virtual ~LBFGSOptimizer () override
 
- Protected Member Functions inherited from itk::SingleValuedNonLinearVnlOptimizer
const CostFunctionAdaptorType * GetCostFunctionAdaptor () const
 
CostFunctionAdaptorType * GetCostFunctionAdaptor ()
 
CostFunctionAdaptorType * GetNonConstCostFunctionAdaptor () const
 
void SetCostFunctionAdaptor (CostFunctionAdaptorType *adaptor)
 
 SingleValuedNonLinearVnlOptimizer ()
 
virtual ~SingleValuedNonLinearVnlOptimizer () override
 
- Protected Member Functions inherited from itk::SingleValuedNonLinearOptimizer
 SingleValuedNonLinearOptimizer ()
 
virtual ~SingleValuedNonLinearOptimizer () override
 
- Protected Member Functions inherited from itk::NonLinearOptimizer
 NonLinearOptimizer ()
 
virtual ~NonLinearOptimizer () override
 
- Protected Member Functions inherited from itk::Optimizer
 Optimizer ()
 
virtual void SetCurrentPosition (const ParametersType &param)
 
virtual ~Optimizer () override
 
- Protected Member Functions inherited from itk::Object
 Object ()
 
bool PrintObservers (std::ostream &os, Indent indent) const
 
virtual void SetTimeStamp (const TimeStamp &time)
 
virtual ~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
 
InternalOptimizerType * m_VnlOptimizer
 

Additional Inherited Members

- Protected Attributes inherited from itk::SingleValuedNonLinearOptimizer
CostFunctionPointer m_CostFunction
 
- Protected Attributes inherited from itk::Optimizer
ParametersType m_CurrentPosition
 
bool m_ScalesInitialized
 
- Protected Attributes inherited from itk::LightObject
AtomicInt< int > m_ReferenceCount
 

Member Typedef Documentation

typedef SmartPointer< const Self > itk::LBFGSOptimizer::ConstPointer

Definition at line 93 of file itkLBFGSOptimizer.h.

typedef Superclass::CostFunctionAdaptorType itk::LBFGSOptimizer::CostFunctionAdaptorType
protected

Definition at line 167 of file itkLBFGSOptimizer.h.

typedef vnl_lbfgs itk::LBFGSOptimizer::InternalOptimizerType

Internal optimizer type.

Definition at line 105 of file itkLBFGSOptimizer.h.

typedef vnl_vector< double > itk::LBFGSOptimizer::InternalParametersType

InternalParameters typedef.

Definition at line 99 of file itkLBFGSOptimizer.h.

typedef SmartPointer< Self > itk::LBFGSOptimizer::Pointer

Definition at line 92 of file itkLBFGSOptimizer.h.

typedef LBFGSOptimizer itk::LBFGSOptimizer::Self

Standard "Self" typedef.

Definition at line 90 of file itkLBFGSOptimizer.h.

typedef SingleValuedNonLinearVnlOptimizer itk::LBFGSOptimizer::Superclass

Definition at line 91 of file itkLBFGSOptimizer.h.

Constructor & Destructor Documentation

itk::LBFGSOptimizer::LBFGSOptimizer ( )
protected
virtual itk::LBFGSOptimizer::~LBFGSOptimizer ( )
overrideprotectedvirtual

Member Function Documentation

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

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

Run-time type information (and related methods).

Reimplemented from itk::SingleValuedNonLinearVnlOptimizer.

vnl_lbfgs* itk::LBFGSOptimizer::GetOptimizer ( )

Method for getting access to the internal optimizer.

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

Get the reason for termination

Reimplemented from itk::Optimizer.

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

Return Current Value

static Pointer itk::LBFGSOptimizer::New ( )
static

Method for creation through the object factory.

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

Print out internal state

Reimplemented from itk::SingleValuedNonLinearVnlOptimizer.

virtual void itk::LBFGSOptimizer::SetCostFunction ( SingleValuedCostFunction *  costFunction)
overridevirtual

Plug in a Cost Function into the optimizer

Implements itk::SingleValuedNonLinearVnlOptimizer.

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

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)
virtual

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)
virtual

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)
virtual

Set/Get the maximum number of function evaluations allowed.

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

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

virtual void itk::LBFGSOptimizer::StartOptimization ( void  )
overridevirtual

Start optimization with an initial value.

Reimplemented from itk::Optimizer.

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

Member Data Documentation

double itk::LBFGSOptimizer::m_DefaultStepLength
private

Definition at line 180 of file itkLBFGSOptimizer.h.

double itk::LBFGSOptimizer::m_GradientConvergenceTolerance
private

Definition at line 178 of file itkLBFGSOptimizer.h.

double itk::LBFGSOptimizer::m_LineSearchAccuracy
private

Definition at line 179 of file itkLBFGSOptimizer.h.

unsigned int itk::LBFGSOptimizer::m_MaximumNumberOfFunctionEvaluations
private

Definition at line 177 of file itkLBFGSOptimizer.h.

bool itk::LBFGSOptimizer::m_OptimizerInitialized
private

Definition at line 170 of file itkLBFGSOptimizer.h.

std::ostringstream itk::LBFGSOptimizer::m_StopConditionDescription
mutableprivate

Definition at line 174 of file itkLBFGSOptimizer.h.

bool itk::LBFGSOptimizer::m_Trace
private

Definition at line 176 of file itkLBFGSOptimizer.h.

InternalOptimizerType* itk::LBFGSOptimizer::m_VnlOptimizer
private

Definition at line 173 of file itkLBFGSOptimizer.h.

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