implements the abstract interface BundleProxObject for $\|y-\hat{y}\|_H^2$ with $H=V\Lambda V^\top+u I$ , i.e., a low rank representation of a symmetric positive definite matrix with the weight times identity added as regularization More...

#include <BundleLowRankTrustRegionProx.hxx>

Inheritance diagram for ConicBundle::BundleLowRankTrustRegionProx:

Public Member Functions
	BundleLowRankTrustRegionProx (CH_Matrix_Classes::Integer dim=0, VariableMetricSelection vp=0, bool local_metric=false, CBout cb=0, int inc=-1)
	default constructor with empty H (equal to zero) and the dimension as argument

	BundleLowRankTrustRegionProx (const CH_Matrix_Classes::Matrix &in_vecH, const CH_Matrix_Classes::Matrix &in_lamH, VariableMetricSelection vp=0, bool local_metric=false, CBout cb=0, int inc=-1)
	constructs H=vecHDiag(lamH)transpose(vecH), so in_lamH must be a column vector with same dimension as columns in in_vecH and the row dimension of in_vecH must match the design space, in_vecH is assumed orthogonal

virtual	~BundleLowRankTrustRegionProx ()
	destructor

void	set_weightu (CH_Matrix_Classes::Real in_weightu)
	sets the next weight

CH_Matrix_Classes::Real	get_weightu () const
	returns the current weight in use

CH_Matrix_Classes::Real	get_term_corr () const
	returns a correction factor for termination precision if the quadratic term is strong

void	init (const CH_Matrix_Classes::Matrix &in_vecH, const CH_Matrix_Classes::Matrix &in_lamH)
	reset the prox information; in_vecH must be an orthogonal matrix with in_vecH.rowdim() matching the dimension but maybe with zero columns; in_lamH must be a column vector with row dimension matching the column dimension of in_vecH and all entries positive

virtual CH_Matrix_Classes::Real	norm_sqr (const CH_Matrix_Classes::Matrix &B) const
	returns $\|B\|^2_H$ (with weight included)

virtual CH_Matrix_Classes::Real	dnorm_sqr (const MinorantPointer &B) const
	returns $\|B\|^2_{H^{-1}}$ (with weight included)

virtual bool	is_DLR () const
	return true if H is of the form diagonal matrix plus Gram matrix of a low rank matrix

virtual int	add_H (CH_Matrix_Classes::Symmatrix &big_sym, CH_Matrix_Classes::Integer start_index=0) const
	add H to the dense symmetric matrix as a principal submatrix starting at position start_index

virtual CH_Matrix_Classes::Matrix &	add_Hx (const CH_Matrix_Classes::Matrix &x, CH_Matrix_Classes::Matrix &outplusHx, CH_Matrix_Classes::Real alpha=1.) const
	adds to outplusHx and returns this

virtual CH_Matrix_Classes::Matrix &	apply_Hinv (CH_Matrix_Classes::Matrix &x) const
	returns $H^{-1}x$ where $H^{-1}=\frac1u(I-V(\Lambda/(\Lambda+u))V^\top)$

virtual void	get_precond (CH_Matrix_Classes::Matrix &inD, const CH_Matrix_Classes::Matrix *&Vp) const
	returns a suitable approximation for preconditioning, see BundleProxObject::get_precond

virtual int	compute_QP_costs (CH_Matrix_Classes::Symmatrix &Q, CH_Matrix_Classes::Matrix &d, CH_Matrix_Classes::Real &offset, const MinorantPointer &constant_minorant, const MinorantBundle &bundle, const CH_Matrix_Classes::Matrix &y, const MinorantPointer &groundset_minorant, CH_Matrix_Classes::Indexmatrix *yfixed)
	computes the dual QP costs Q, d, and the constant offset to the bundle subproblem, see BundleProxObject::compute_QP_costs

virtual int	update_QP_costs (CH_Matrix_Classes::Symmatrix &delta_Q, CH_Matrix_Classes::Matrix &delta_d, CH_Matrix_Classes::Real &delta_offset, const MinorantPointer &constant_minorant, const MinorantBundle &bundle, const CH_Matrix_Classes::Matrix &center_y, const MinorantPointer &groundset_minorant, const MinorantPointer &delta_groundset_minorant, const CH_Matrix_Classes::Indexmatrix &delta_index, CH_Matrix_Classes::Indexmatrix *yfixed)
	updates the dual QP costs Q, d, and the constant offset to the bundle subproblem, see BundleProxObject::update_QP_costs

virtual int	apply_modification (const GroundsetModification &gsmdf)
	when BundleSolver is called to modify the groundset it also calls this

virtual BundleProxObject *	projected_clone (const CH_Matrix_Classes::Indexmatrix &indices)
	in order to allow for fixed variables, this generates a clone restricted to the given indices

virtual bool	supports_diagonal_bounds_scaling () const
	this implementation does not support a diagonal scaling heuristic, therefore the following routine has to return true.

virtual int	diagonal_scaling_heuristic_update (const CH_Matrix_Classes::Matrix &)
	if supported, D_update has to contain nonnegative numbers that are permanently added to the diagonal here. It is important to keep track of this change only if afterwards update_QP_costs is called before compute_QP_costs. In this case the only nonzero enries in D_update must be those of delta_index

virtual bool	supports_dense_variable_metric () const
	returns true if dynamic scaling with dense symmetric matrices is supported

virtual bool	supports_lowrank_variable_metric () const
	returns true if dynamic scaling with low rank structure is supported

virtual bool	supports_diagonal_variable_metric () const
	returns true if dynamic scaling with diagonal matrices is supported

virtual int	apply_variable_metric (VariableMetricModel groundset, VariableMetricModel model, const CH_Matrix_Classes::Matrix &aggr, CH_Matrix_Classes::Integer y_id, const CH_Matrix_Classes::Matrix &y, bool descent_step, CH_Matrix_Classes::Real &current_weight, CH_Matrix_Classes::Real model_maxviol, const CH_Matrix_Classes::Indexmatrix *new_indices=0)
	see DynamicProx

virtual int	add_variable_metric (CH_Matrix_Classes::Matrix &diagH, CH_Matrix_Classes::Matrix &vecH)
	see BundleProxObject::add_dynamic_scaling()

virtual int	push_aft (const AffineFunctionTransformation *aft)
	see BundleProxObject::push_aft();

virtual int	pop_aft ()
	see BundleProxObject::pop_aft();

virtual int	mfile_data (std::ostream &out) const
	output the description of the prox term in mfile-suitable format

Public Member Functions inherited from ConicBundle::BundleProxObject
	BundleProxObject (VariableMetricSelection vp=0, bool local_scaling=false, bool bounds_scaling=false, CBout cb=0, int cbincr=-1)
	default constructor, switching on dynamic scaling only works for classes with corresponding support

virtual void	set_short_QPsteps (CH_Matrix_Classes::Integer shortQPst)
	may be used to indicate seemingly conservative step sizes possibly due to the quadratic term

virtual CH_Matrix_Classes::Integer	get_short_QPsteps ()
	retrieves the number of conservative step sizes possibly due to the quadratic term passed on to this

int	apply_factor (CH_Matrix_Classes::Real f)
	allows AFTModel and SumModel to accumulate a compensation factor for tracing the effects of recursive applications of function_factor in update_model (does not affect H but can be retrieved by get_factor() for this purpose)

CH_Matrix_Classes::Real	get_factor ()
	returns the current accumulated compensation factor by which H would need to be scaled in order to reflect the curvature relative to the current function without function_factor;

Public Member Functions inherited from ConicBundle::VariableMetric
virtual	~VariableMetric ()
	virtual destructor

	VariableMetric (VariableMetricSelection vp=0, bool use_loc_metric=false, bool use_bnds_scaling=false, CBout cbo=0, int cbinc=-1)
	default constructor; if vp is not zero, ownership of vp is passed over to this and *this will delete vp

VariableMetricSelection *	get_variable_metric_selection () const
	returns 0 or an available VariableMetricSelection object, that may be employed for computing a variable metric term in accordance with the value of use_local_metric

void	set_variable_metric_selection (VariableMetricSelection *vp=0)
	sets use_variable_metric; the object passed is then owned by this

bool	employ_variable_metric () const
	returns true if some dynamic scaling is supported and switched on

virtual int	add_variable_metric (CH_Matrix_Classes::Symmatrix &)
	adds a suitable modification of symH (symH may be modified in this) to the scaling matrix H More...

bool	get_use_bounds_scaling () const
	returns use_bounds_scaling

void	set_use_bounds_scaling (bool bounds_scaling)
	sets use_bounds_scaling

bool	employ_diagonal_bounds_scaling () const
	if the respective implementation supports a diagonal bounds scaling heuristic, the following routine has to return true; see also diagonal_bounds_scaling_update()

virtual int	diagonal_bounds_scaling_update (const CH_Matrix_Classes::Matrix &)
	if supported, D_update has to contain nonnegative numbers that are permanently added to the diagonal here. More...

bool	get_use_local_metric () const
	returns use_local_metric

void	set_use_local_metric (bool local_metric)
	sets use_local_metric

Public Member Functions inherited from ConicBundle::CBout
virtual void	set_out (std::ostream *out=0, int print_level=1)
	Specifies the output level (out==NULL: no output at all, out!=NULL and level=0: errors and warnings, level>0 increasingly detailed information) More...

virtual void	set_cbout (const CBout *cb, int incr=-1)
	Specifies the output level relative to the given CBout class. More...

void	clear_cbout ()
	reset to default settings (out=0,print_level=1)

	CBout (const CBout *cb=0, int incr=-1)
	calls set_cbout

	CBout (std::ostream *outp, int pl=1)
	initialize correspondingly

	CBout (const CBout &cb, int incr=0)
	copy constructor

virtual bool	cb_out (int pl=-1) const
	Returns true if out!=0 and (pl<print_level), pl<0 should be used for WARNINGS and ERRORS only, pl==0 for usual output.

std::ostream &	get_out () const
	If cb_out() returned true, this returns the output stream, but it will abort if called with out==0.

std::ostream *	get_out_ptr () const
	returns the pointer to the output stream

int	get_print_level () const
	returns the print_level

Public Member Functions inherited from ConicBundle::QPSolverProxObject
virtual	~QPSolverProxObject ()
	virtual destructor

Private Member Functions
void	clean ()
	if not clean this orthogonalizes vecH and trucates lamH

void	compute_corr ()
	computes the correction value, here min(1,dim/trace(H))

Private Attributes
CH_Matrix_Classes::Real	weightu
	the current weight added to H in the form of weightu*I

CH_Matrix_Classes::Matrix	vecH
	orthonormal columns for the low rank representation

CH_Matrix_Classes::Matrix	lamH
	positive definite scalars for the diagonal vecHDiag(lamH)transpose(vecH)

CH_Matrix_Classes::Matrix	scaled_vecH
	vecH*Diag(sqrt(lamH)) for use in preconditioning

CH_Matrix_Classes::Matrix	lamHi
	the diagonal weights adapted for the low rank inverse

CH_Matrix_Classes::Matrix	sqrtlamHi
	the square root of the diagonal weights adapted for the low rank inverse

CH_Matrix_Classes::Real	corr_val
	the correction value for correcting termination precision

CH_Matrix_Classes::Indexmatrix	old_fixed_ind
	the fixed indices for which the QP_costs were computed

CH_Matrix_Classes::Matrix	_A
	for compute_QP_costs() this holds the subgradients with zeroed fixed parts

CH_Matrix_Classes::Matrix	_b
	for compute_QP_costs() this holds the constant subgradient with zeroed fixed parts

CH_Matrix_Classes::Matrix	_c
	for compute_QP_costs() this holds the offset values including fixed contributions

CH_Matrix_Classes::Real	_delta
	for compute_QP_costs() this holds the constant offset including fixed contributions

CH_Matrix_Classes::Matrix	_y
	for compute_QP_costs() this holds the non_fixed part of center_y

CH_Matrix_Classes::Matrix	LinvindHt
	for compute_QP_costs() this holds L^{-1}* vecH^T for non fixed indices

CH_Matrix_Classes::Symmatrix	old_LinvQ
	the old quadratic cost matrix dependent on the low rank part

CH_Matrix_Classes::Matrix	oldd
	the old linear cost term;

CH_Matrix_Classes::Real	oldoffset
	the old costant cost term;

const CH_Matrix_Classes::Indexmatrix *	new_indices
	if values should be computed for a new subset indices, this is stored here

std::vector< const AffineFunctionTransformation * >	aft_stack
	in add_variable_metric() the stack serves to transform the given data

bool	needs_cleaning
	flag for variable metric, whether columns have been orthogonalized and lam truncated

CH_Matrix_Classes::Integer	max_columns
	for variable metric this gives an upper bound for collecting columns before cleaning

Additional Inherited Members
Protected Attributes inherited from ConicBundle::BundleProxObject
CH_Matrix_Classes::Real	factor
	used to accumulate a compensation factor for function_factor; this factor is not included in H but can be applied externally via get_factor() if required

CH_Matrix_Classes::Integer	short_QPsteps
	the QP may signal short steps that seem due to the quadratic term by setting this counter via set_short_QPsteps()

Static Protected Attributes inherited from ConicBundle::BundleProxObject
static const CH_Matrix_Classes::Integer	xdim_threshold = 100
	constant for possible use if QP coefficients are to be computed in parallel (still purely experimental)

Detailed Description

implements the abstract interface BundleProxObject for $\|y-\hat{y}\|_H^2$ with $H=V\Lambda V^\top+u I$ , i.e., a low rank representation of a symmetric positive definite matrix with the weight times identity added as regularization

The regularized low rank representation reads $H=rI+V\Lambda V^T$ where $r>0$ is a scalar regularization parameter, $I$ is the identity, $\Lambda$ is a strictly positive diagonal matrix and the orthogonal matrix $V$ holds the corresponding column vectors.

For this the inverse is formed via a QR-variant for numerical stability.

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

BundleLowRankTrustRegionProx.hxx

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description