Implementation of the HessianUpdater for limit-memory quasi-Newton approximation of the Lagrangian Hessian. More...

#include <IpLimMemQuasiNewtonUpdater.hpp>

Inheritance diagram for Ipopt::LimMemQuasiNewtonUpdater:

Public Member Functions
virtual bool	InitializeImpl (const OptionsList &options, const std::string &prefix)
	overloaded from AlgorithmStrategyObject

virtual void	UpdateHessian ()
	Update the Hessian based on the current information in IpData.

Constructors / Destructors
	LimMemQuasiNewtonUpdater (bool update_for_resto)
	Default Constructor.

virtual	~LimMemQuasiNewtonUpdater ()
	Destructor.

Public Member Functions inherited from Ipopt::HessianUpdater
	HessianUpdater ()
	Default Constructor.

virtual	~HessianUpdater ()
	Destructor.

Public Member Functions inherited from Ipopt::AlgorithmStrategyObject
bool	Initialize (const Journalist &jnlst, IpoptNLP &ip_nlp, IpoptData &ip_data, IpoptCalculatedQuantities &ip_cq, const OptionsList &options, const std::string &prefix)
	This method is called every time the algorithm starts again - it is used to reset any internal state.

bool	ReducedInitialize (const Journalist &jnlst, const OptionsList &options, const std::string &prefix)
	Reduced version of the Initialize method, which does not require special Ipopt information.

	AlgorithmStrategyObject ()
	Default Constructor.

virtual	~AlgorithmStrategyObject ()
	Destructor.

Public Member Functions inherited from Ipopt::ReferencedObject
	ReferencedObject ()

virtual	~ReferencedObject ()

Index	ReferenceCount () const

void	AddRef (const Referencer *referencer) const

void	ReleaseRef (const Referencer *referencer) const

Static Public Member Functions

static void	RegisterOptions (SmartPtr< RegisteredOptions > roptions)
	Methods for OptionsList.

Private Member Functions
Default Compiler Generated Methods
(Hidden to avoid implicit creation/calling). These methods are not implemented and we do not want the compiler to implement them for us, so we declare them private and do not define them. This ensures that they will not be implicitly created/called.
	LimMemQuasiNewtonUpdater (const LimMemQuasiNewtonUpdater &)
	Copy Constructor.

void	operator= (const LimMemQuasiNewtonUpdater &)
	Default Assignment Operator.

Auxiliary function
bool	CheckSkippingBFGS (const Vector &s_new, const Vector &y_new)
	Method deciding whether the BFGS update should be skipped.

bool	UpdateInternalData (const Vector &s_new, const Vector &y_new, SmartPtr< Vector > ypart_new)
	Update the internal data, such as the S, Y, L, D etc matrices and vectors that are required for computing the compact representation.

void	AugmentMultiVector (SmartPtr< MultiVectorMatrix > &V, const Vector &v_new)
	Given a MutliVector V, create a new MultiVectorSpace with one more column, and return V as a member of that space, consisting of all previous vectors, and in addition v_new in the last column.

void	AugmentDenseVector (SmartPtr< DenseVector > &V, Number v_new)
	Given a DenseVector V, create a new DenseVectorSpace with one more row, and return V as a member of that space, consisting of all previous elements, and in addition v_new in the last row.

void	AugmentLMatrix (SmartPtr< DenseGenMatrix > &V, const MultiVectorMatrix &S, const MultiVectorMatrix &Y)
	Given a strictly-lower triangular square DenseGenMatrix V, create a new DenseGenMatrixSpace with one more dimension, and return V as a member of that space, consisting of all previous elements, and in addition elements s_i^Ty_j for (i<j), where s and y are the vectors in the MultiVectors S and Y.

void	AugmentSdotSMatrix (SmartPtr< DenseSymMatrix > &V, const MultiVectorMatrix &S)
	Given a DenseSymMatrix V, create a new DenseGenMatrixSpace with one more dimension, and return V as a member of that space, consisting of all previous elements, and in addition elements s_i^Ts_j for the new entries, where s are the vectors in the MultiVector S.

void	AugmentSTDRSMatrix (SmartPtr< DenseSymMatrix > &V, const MultiVectorMatrix &S, const MultiVectorMatrix &DRS)
	Given a DenseSymMatrix V, create a new DenseGenMatrixSpace with one more dimension, and return V as a member of that space, consisting of all previous elements, and in addition elements s_i^TDRs_j for the new entries, where s are the vectors in the MultiVector S, and DRs are the vectors in DRS.

void	ShiftMultiVector (SmartPtr< MultiVectorMatrix > &V, const Vector &v_new)
	Given a MutliVector V, get rid of the first column, shift all other columns to the left, and make v_new the last column.

void	ShiftDenseVector (SmartPtr< DenseVector > &V, Number v_new)
	Given a DenseVector V, get rid of the first element, shift all other elements one position to the top, and make v_new the last entry.

void	ShiftLMatrix (SmartPtr< DenseGenMatrix > &V, const MultiVectorMatrix &S, const MultiVectorMatrix &Y)
	Given a strictly-lower triangular square DenseGenMatrix V, shift everything one row and column up, and fill the new strictly lower triangular entries as s_i^Ty_j for (i<j), where s and y are the vectors in the MultiVectors S and Y.

void	ShiftSdotSMatrix (SmartPtr< DenseSymMatrix > &V, const MultiVectorMatrix &S)
	Given a DenseSymMatrix V, shift everything up one row and column, and fill the new entries as s_i^Ts_j, where s are the vectors in the MultiVector S.

void	ShiftSTDRSMatrix (SmartPtr< DenseSymMatrix > &V, const MultiVectorMatrix &S, const MultiVectorMatrix &DRS)
	Given a DenseSymMatrix V, shift everything up one row and column, and fill the new entries as s_i^TDRs_j, where s are the vectors in the MultiVector S, and DRs are the vectors in DRS.

void	RecalcY (Number eta, const Vector &DR_x, MultiVectorMatrix &S, MultiVectorMatrix &Ypart, SmartPtr< MultiVectorMatrix > &Y)
	Method for recomputing Y from scratch, using Ypart (only for restoration phase)

void	RecalcD (const MultiVectorMatrix &S, const MultiVectorMatrix &Y, SmartPtr< DenseVector > &D)
	Method for recomputing D from S and Y.

void	RecalcL (const MultiVectorMatrix &S, const MultiVectorMatrix &Y, SmartPtr< DenseGenMatrix > &L)
	Method for recomputing L from S and Y.

bool	SplitEigenvalues (DenseGenMatrix &Q, const DenseVector &E, SmartPtr< DenseGenMatrix > &Qminus, SmartPtr< DenseGenMatrix > &Qplus)
	Split the eigenvectors into negative and positive ones.

void	StoreInternalDataBackup ()
	Store a copy of the pointers to the internal data (S, Y, D, L, SdotS, curr_lm_memory).

void	RestoreInternalDataBackup ()
	Restore the copy of the pointers to the internal data most recently stored with StoreInternalDataBackup().

void	SetW ()
	Release anything that we allocated for StoreInternalDataBackup and is no longer needed.

Private Attributes
SmartPtr< const LowRankUpdateSymMatrixSpace >	h_space_
	Matrix space for the low-rank Hessian approximation.

const bool	update_for_resto_
	Flag indicating if the update is to be done for the original NLP or for the restoration phase NLP.

Number	last_eta_
	Most recent value for eta in the restoration phase objective function (only for update_for_resto_ = true)

SmartPtr< const Vector >	curr_DR_x_
	Current DR_x scaling factors in the restoration phase objective function (only for update_for_resto_ = true).

TaggedObject::Tag	curr_DR_x_tag_
	Tag for curr_DR_x_.

SmartPtr< const Vector >	curr_red_DR_x_
	Current DR_x scaling factors in the restoration phase objective function in the smaller space for the approximation.

Number	curr_eta_
	Current value of weighing factor eta in the restoration phase objective function (only for update_for_resto_ = true)

Index	lm_skipped_iter_
	Counter for successive iterations in which the update was skipped.

Information for the limited memory update
Index	curr_lm_memory_
	current size of limited memory

SmartPtr< MultiVectorMatrix >	S_
	s pairs for the recent iterations

SmartPtr< MultiVectorMatrix >	Y_
	y pairs for the recent iterations.

SmartPtr< MultiVectorMatrix >	Ypart_
	For restoration phase update: Y without the quadratic objective function part.

SmartPtr< DenseVector >	D_
	Diagonal elements D_k for compact formulation from last update.

SmartPtr< DenseGenMatrix >	L_
	Matrix L_k for compact formulation from last update.

SmartPtr< Vector >	B0_
	First term (starting matrix) for the approximation.

Number	sigma_
	First term (starting matrix) for the approximation.

SmartPtr< MultiVectorMatrix >	V_
	V in LowRankUpdateMatrix from last update.

SmartPtr< MultiVectorMatrix >	U_
	U in LowRankUpdateMatrix from last update.

SmartPtr< DenseSymMatrix >	SdotS_
	For efficient implementation, we store the pairwise products for s's.

bool	SdotS_uptodate_
	Flag indicating whether SdotS_ is update to date from most recent update.

SmartPtr< MultiVectorMatrix >	DRS_
	DR * S (only for restoration phase)

SmartPtr< DenseSymMatrix >	STDRS_
	For efficient implementation, we store the S^T S DR * S.

SmartPtr< const Vector >	last_x_
	Primal variables x from most recent update.

SmartPtr< const Vector >	last_grad_f_
	Gradient of objective function w.r.t.

SmartPtr< const Matrix >	last_jac_c_
	Jacobian for equality constraints w.r.t x at x_last.

SmartPtr< const Matrix >	last_jac_d_
	Jacobian for inequality constraints w.r.t x at x_last.

Index	curr_lm_memory_old_
	current size of limited memory

SmartPtr< MultiVectorMatrix >	S_old_
	s pairs for the recent iterations (backup)

SmartPtr< MultiVectorMatrix >	Y_old_
	y pairs for the recent iterations.

SmartPtr< MultiVectorMatrix >	Ypart_old_
	For restoration phase update: Y without the quadratic objective function part (backup)

SmartPtr< DenseVector >	D_old_
	Diagonal elements D_k for compact formulation from last update (backup).

SmartPtr< DenseGenMatrix >	L_old_
	Matrix L_k for compact formulation from last update (backup).

SmartPtr< Vector >	B0_old_
	First term (starting matrix) for the approximation (backup).

Number	sigma_old_
	First term (starting matrix) for the approximation.

SmartPtr< MultiVectorMatrix >	V_old_
	V in LowRankUpdateMatrix from last update (backup)

SmartPtr< MultiVectorMatrix >	U_old_
	U in LowRankUpdateMatrix from last update (backup)

SmartPtr< DenseSymMatrix >	SdotS_old_
	For efficient implementation, we store the pairwise products for s's (backup).

bool	SdotS_uptodate_old_
	Flag indicating whether SdotS_ is update to date from most recent update (backup).

SmartPtr< MultiVectorMatrix >	DRS_old_
	DR * S (only for restoration phase) (backup)

SmartPtr< DenseSymMatrix >	STDRS_old_
	For efficient implementation, we store the S^T S DR * S.

Algorithmic parameters
enum	LMUpdateType { BFGS = 0 , SR1 }
	enumeration for the Hessian update type. More...

enum	LMInitialization { SCALAR1 = 0 , SCALAR2 , SCALAR3 , SCALAR4 , CONSTANT }
	enumeration for the Hessian initialization. More...

Index	limited_memory_max_history_
	Size of memory for limited memory update.

LMUpdateType	limited_memory_update_type_
	Type of Hessian update.

LMInitialization	limited_memory_initialization_
	How to choose B0 in the low-rank update.

Number	limited_memory_init_val_
	Value of B0 (as this multiple of the identity in certain situations).

Index	limited_memory_max_skipping_
	Number of successive iterations of skipped updates after which the approximation is reset.

Number	sigma_safe_min_
	Minimal safeguard value for sigma.

Number	sigma_safe_max_
	Maximal safeguard value for sigma.

bool	limited_memory_special_for_resto_
	Flag indicating if Hessian approximation should be done in a special manner for the restoration phase.

Additional Inherited Members
Protected Member Functions inherited from Ipopt::AlgorithmStrategyObject
const Journalist &	Jnlst () const

IpoptNLP &	IpNLP () const

IpoptData &	IpData () const

IpoptCalculatedQuantities &	IpCq () const

bool	HaveIpData () const

Detailed Description

Implementation of the HessianUpdater for limit-memory quasi-Newton approximation of the Lagrangian Hessian.

Definition at line 23 of file IpLimMemQuasiNewtonUpdater.hpp.

Member Enumeration Documentation

◆ LMUpdateType

enum Ipopt::LimMemQuasiNewtonUpdater::LMUpdateType

private

enumeration for the Hessian update type.

Enumerator
BFGS
SR1

Definition at line 84 of file IpLimMemQuasiNewtonUpdater.hpp.

◆ LMInitialization

enum Ipopt::LimMemQuasiNewtonUpdater::LMInitialization

private

enumeration for the Hessian initialization.

Enumerator
SCALAR1
SCALAR2
SCALAR3
SCALAR4
CONSTANT

Definition at line 94 of file IpLimMemQuasiNewtonUpdater.hpp.

Constructor & Destructor Documentation

◆ LimMemQuasiNewtonUpdater() [1/2]

Ipopt::LimMemQuasiNewtonUpdater::LimMemQuasiNewtonUpdater ( bool update_for_resto )

Default Constructor.

◆ ~LimMemQuasiNewtonUpdater()

virtual Ipopt::LimMemQuasiNewtonUpdater::~LimMemQuasiNewtonUpdater ( )

inlinevirtual

Destructor.

Definition at line 34 of file IpLimMemQuasiNewtonUpdater.hpp.

◆ LimMemQuasiNewtonUpdater() [2/2]

Ipopt::LimMemQuasiNewtonUpdater::LimMemQuasiNewtonUpdater ( const LimMemQuasiNewtonUpdater & )

private

Copy Constructor.

Member Function Documentation

◆ InitializeImpl()

virtual bool Ipopt::LimMemQuasiNewtonUpdater::InitializeImpl	(	const OptionsList &	options,
		const std::string &	prefix
	)

virtual

overloaded from AlgorithmStrategyObject

Implements Ipopt::HessianUpdater.

◆ UpdateHessian()

virtual void Ipopt::LimMemQuasiNewtonUpdater::UpdateHessian ( )

virtual

Update the Hessian based on the current information in IpData.

Implements Ipopt::HessianUpdater.

◆ RegisterOptions()

static void Ipopt::LimMemQuasiNewtonUpdater::RegisterOptions ( SmartPtr< RegisteredOptions > roptions )

static

Methods for OptionsList.

◆ operator=()

void Ipopt::LimMemQuasiNewtonUpdater::operator= ( const LimMemQuasiNewtonUpdater & )

private

Default Assignment Operator.

◆ CheckSkippingBFGS()

bool Ipopt::LimMemQuasiNewtonUpdater::CheckSkippingBFGS	(	const Vector &	s_new,
		const Vector &	y_new
	)

private

Method deciding whether the BFGS update should be skipped.

If Powell-damping is performed, the Vectors s_new and y_new might be adapted.

Returns: true, if no update is to be performed this time.

◆ UpdateInternalData()

bool Ipopt::LimMemQuasiNewtonUpdater::UpdateInternalData	(	const Vector &	s_new,
		const Vector &	y_new,
		SmartPtr< Vector >	ypart_new
	)

private

Update the internal data, such as the S, Y, L, D etc matrices and vectors that are required for computing the compact representation.

Returns: true, if the limited memory history grew (i.e., curr_lm_memory_ was increased).

◆ AugmentMultiVector()

void Ipopt::LimMemQuasiNewtonUpdater::AugmentMultiVector	(	SmartPtr< MultiVectorMatrix > &	V,
		const Vector &	v_new
	)

private

Given a MutliVector V, create a new MultiVectorSpace with one more column, and return V as a member of that space, consisting of all previous vectors, and in addition v_new in the last column.

If V is NULL, then a new MatrixSpace with one column is created.

◆ AugmentDenseVector()

void Ipopt::LimMemQuasiNewtonUpdater::AugmentDenseVector	(	SmartPtr< DenseVector > &	V,
		Number	v_new
	)

private

Given a DenseVector V, create a new DenseVectorSpace with one more row, and return V as a member of that space, consisting of all previous elements, and in addition v_new in the last row.

If V is NULL, then a new DenseVectorSpace with dimension one is created.

◆ AugmentLMatrix()

void Ipopt::LimMemQuasiNewtonUpdater::AugmentLMatrix	(	SmartPtr< DenseGenMatrix > &	V,
		const MultiVectorMatrix &	S,
		const MultiVectorMatrix &	Y
	)

private

Given a strictly-lower triangular square DenseGenMatrix V, create a new DenseGenMatrixSpace with one more dimension, and return V as a member of that space, consisting of all previous elements, and in addition elements s_i^Ty_j for (i<j), where s and y are the vectors in the MultiVectors S and Y.

If V is NULL, then a new DenseGenMatrixSpace with dimension one is created.

◆ AugmentSdotSMatrix()

void Ipopt::LimMemQuasiNewtonUpdater::AugmentSdotSMatrix	(	SmartPtr< DenseSymMatrix > &	V,
		const MultiVectorMatrix &	S
	)

private

Given a DenseSymMatrix V, create a new DenseGenMatrixSpace with one more dimension, and return V as a member of that space, consisting of all previous elements, and in addition elements s_i^Ts_j for the new entries, where s are the vectors in the MultiVector S.

If V is NULL, then a new DenseGenMatrixSpace with dimension one is created.

◆ AugmentSTDRSMatrix()

void Ipopt::LimMemQuasiNewtonUpdater::AugmentSTDRSMatrix	(	SmartPtr< DenseSymMatrix > &	V,
		const MultiVectorMatrix &	S,
		const MultiVectorMatrix &	DRS
	)

private

Given a DenseSymMatrix V, create a new DenseGenMatrixSpace with one more dimension, and return V as a member of that space, consisting of all previous elements, and in addition elements s_i^TDRs_j for the new entries, where s are the vectors in the MultiVector S, and DRs are the vectors in DRS.

If V is NULL, then a new DenseGenMatrixSpace with dimension one is created.

◆ ShiftMultiVector()

void Ipopt::LimMemQuasiNewtonUpdater::ShiftMultiVector	(	SmartPtr< MultiVectorMatrix > &	V,
		const Vector &	v_new
	)

private

Given a MutliVector V, get rid of the first column, shift all other columns to the left, and make v_new the last column.