Composite \(\ell_1\)-penalty function \( \|c(x)\|_1 \). More...

#include <aligator/modelling/constraints/l1-penalty.hpp>

Inheritance diagram for aligator::NonsmoothPenaltyL1Tpl< _Scalar >:

Collaboration diagram for aligator::NonsmoothPenaltyL1Tpl< _Scalar >:

Public Types
using	Scalar = _Scalar

using	Base = ConstraintSetTpl<Scalar>

using	ActiveType = typename Base::ActiveType

Public Types inherited from aligator::ConstraintSetTpl< _Scalar >
using	Scalar = _Scalar

using	ActiveType = Eigen::Matrix<bool, Eigen::Dynamic, 1>

Public Member Functions
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)

	NonsmoothPenaltyL1Tpl ()=default

	NonsmoothPenaltyL1Tpl (const NonsmoothPenaltyL1Tpl &)=default

NonsmoothPenaltyL1Tpl &	operator= (const NonsmoothPenaltyL1Tpl &)=default

	NonsmoothPenaltyL1Tpl (NonsmoothPenaltyL1Tpl &&)=default

NonsmoothPenaltyL1Tpl &	operator= (NonsmoothPenaltyL1Tpl &&)=default

Scalar	evaluate (const ConstVectorRef &zproj) const

decltype(auto)	projection_impl (const ConstVectorRef &z) const

void	projection (const ConstVectorRef &z, VectorRef zout) const
	Compute projection of variable `z` onto the constraint set.

void	normalConeProjection (const ConstVectorRef &z, VectorRef zout) const
	Compute projection of `z` onto the normal cone to the set. The default implementation is just \( \mathrm{id} - P\).

void	computeActiveSet (const ConstVectorRef &z, Eigen::Ref< ActiveType > out) const

Public Member Functions inherited from aligator::ConstraintSetTpl< _Scalar >
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)

	ConstraintSetTpl ()=default

virtual bool	disableGaussNewton () const

virtual void	applyProjectionJacobian (const ConstVectorRef &z, MatrixRef Jout) const
	Apply a jacobian of the projection/proximal operator to a matrix.

virtual void	applyNormalConeProjectionJacobian (const ConstVectorRef &z, MatrixRef Jout) const
	Apply the jacobian of the projection on the normal cone.

void	setProxParameter (const Scalar mu) const
	Update proximal parameter; this applies to when this class is a proximal operator that isn't a projection (e.g. \( \ell_1 \)).

virtual	~ConstraintSetTpl ()=default

bool	operator== (const ConstraintSetTpl< Scalar > &rhs)

Scalar	evaluateMoreauEnvelope (const ConstVectorRef &zin, const ConstVectorRef &zproj) const
	Evaluate the Moreau envelope with parameter `mu` for the given contraint set or nonsmooth penalty \(g\) at point `zin`.

Scalar	computeMoreauEnvelope (const ConstVectorRef &zin, VectorRef zprojout) const
	Evaluate the Moreau envelope with parameter `mu` for the given contraint set or nonsmooth penalty \(g\) at point `zin`. This variant evaluates the prox map.

Scalar	mu () const

Scalar	mu_inv () const

Public Attributes
Scalar	mu_

Additional Inherited Members
Protected Attributes inherited from aligator::ConstraintSetTpl< _Scalar >
Scalar	mu_ = 0.

Scalar	mu_inv_

Detailed Description

template<typename _Scalar>
struct aligator::NonsmoothPenaltyL1Tpl< _Scalar >

Composite \(\ell_1\)-penalty function \( \|c(x)\|_1 \).

The composite \(\ell_1\)-penalty penalizes the norm \( \| r(x) \|_1\) of a residual function. This class implements the proximity operator (soft-thresholding) and an appropriate generalized Jacobian.

Definition at line 18 of file l1-penalty.hpp.

Member Typedef Documentation

◆ Scalar

template<typename _Scalar>

using aligator::NonsmoothPenaltyL1Tpl< _Scalar >::Scalar = _Scalar

Definition at line 19 of file l1-penalty.hpp.

◆ Base

template<typename _Scalar>

using aligator::NonsmoothPenaltyL1Tpl< _Scalar >::Base = ConstraintSetTpl<Scalar>

Definition at line 28 of file l1-penalty.hpp.

◆ ActiveType

template<typename _Scalar>

using aligator::NonsmoothPenaltyL1Tpl< _Scalar >::ActiveType = typename Base::ActiveType

Definition at line 29 of file l1-penalty.hpp.

Constructor & Destructor Documentation

◆ NonsmoothPenaltyL1Tpl() [1/3]

template<typename _Scalar>

aligator::NonsmoothPenaltyL1Tpl< _Scalar >::NonsmoothPenaltyL1Tpl ( )

default

◆ NonsmoothPenaltyL1Tpl() [2/3]

template<typename _Scalar>

aligator::NonsmoothPenaltyL1Tpl< _Scalar >::NonsmoothPenaltyL1Tpl ( const NonsmoothPenaltyL1Tpl< _Scalar > & )

default

◆ NonsmoothPenaltyL1Tpl() [3/3]

template<typename _Scalar>

aligator::NonsmoothPenaltyL1Tpl< _Scalar >::NonsmoothPenaltyL1Tpl ( NonsmoothPenaltyL1Tpl< _Scalar > && )

default

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

template<typename _Scalar>

aligator::NonsmoothPenaltyL1Tpl< _Scalar >::ALIGATOR_DYNAMIC_TYPEDEFS ( Scalar )

◆ operator=() [1/2]

template<typename _Scalar>

NonsmoothPenaltyL1Tpl & aligator::NonsmoothPenaltyL1Tpl< _Scalar >::operator= ( const NonsmoothPenaltyL1Tpl< _Scalar > & )

default

◆ operator=() [2/2]

template<typename _Scalar>

NonsmoothPenaltyL1Tpl & aligator::NonsmoothPenaltyL1Tpl< _Scalar >::operator= ( NonsmoothPenaltyL1Tpl< _Scalar > && )

default

◆ evaluate()

template<typename _Scalar>

Scalar aligator::NonsmoothPenaltyL1Tpl< _Scalar >::evaluate ( const ConstVectorRef & ) const

inlinevirtual

Provided the image zproj by the proximal/projection map, evaluate the nonsmooth penalty or constraint set indicator function.

Note: This will be 0 for projection operators.

Reimplemented from aligator::ConstraintSetTpl< _Scalar >.

Definition at line 32 of file l1-penalty.hpp.

◆ projection_impl()

template<typename _Scalar>

decltype(auto) aligator::NonsmoothPenaltyL1Tpl< _Scalar >::projection_impl ( const ConstVectorRef & z ) const

inline

Definition at line 36 of file l1-penalty.hpp.

◆ projection()

template<typename _Scalar>

void aligator::NonsmoothPenaltyL1Tpl< _Scalar >::projection	(	const ConstVectorRef &	z,
		VectorRef	zout ) const

inlinevirtual

Compute projection of variable z onto the constraint set.

Parameters

[in]	z	Input vector
[out]	zout	Output projection

Implements aligator::ConstraintSetTpl< _Scalar >.

Definition at line 41 of file l1-penalty.hpp.

◆ normalConeProjection()

template<typename _Scalar>

void aligator::NonsmoothPenaltyL1Tpl< _Scalar >::normalConeProjection	(	const ConstVectorRef &	z,
		VectorRef	zout ) const

inlinevirtual

Compute projection of z onto the normal cone to the set. The default implementation is just \( \mathrm{id} - P\).

Parameters

[in]	z	Input vector
[out]	zout	Output projection on the normal projection

Implements aligator::ConstraintSetTpl< _Scalar >.

Definition at line 45 of file l1-penalty.hpp.

◆ computeActiveSet()

template<typename _Scalar>

void aligator::NonsmoothPenaltyL1Tpl< _Scalar >::computeActiveSet	(	const ConstVectorRef &	z,
		Eigen::Ref< ActiveType >	out ) const

inlinevirtual

Compute the active set of the constraint. Active means the Jacobian of the proximal operator is nonzero.

Implements aligator::ConstraintSetTpl< _Scalar >.

Definition at line 49 of file l1-penalty.hpp.

Member Data Documentation

◆ mu_

template<typename _Scalar>

Scalar aligator::ConstraintSetTpl< Scalar >::mu_

mutable

Definition at line 112 of file constraint-set.hpp.

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

include/aligator/modelling/constraints/l1-penalty.hpp

Public Types

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Scalar

◆ Base

◆ ActiveType

Constructor & Destructor Documentation

◆ NonsmoothPenaltyL1Tpl() [1/3]

◆ NonsmoothPenaltyL1Tpl() [2/3]

◆ NonsmoothPenaltyL1Tpl() [3/3]

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ evaluate()

◆ projection_impl()

◆ projection()

◆ normalConeProjection()

◆ computeActiveSet()

Member Data Documentation

◆ mu_