Base constraint set type. More...

#include <aligator/core/constraint-set.hpp>

Inheritance diagram for aligator::ConstraintSetTpl< _Scalar >:

Public Types
using	Scalar = _Scalar

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

Public Member Functions
	ALIGATOR_DYNAMIC_TYPEDEFS (Scalar)

	ConstraintSetTpl ()=default

virtual bool	disableGaussNewton () const

virtual Scalar	evaluate (const ConstVectorRef &) const

virtual void	projection (const ConstVectorRef &z, VectorRef zout) const =0
	Compute projection of variable `z` onto the constraint set.

virtual void	normalConeProjection (const ConstVectorRef &z, VectorRef zout) const =0
	Compute projection of `z` onto the normal cone to the set. The default implementation is just \( \mathrm{id} - P\).

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 void	computeActiveSet (const ConstVectorRef &z, Eigen::Ref< ActiveType > out) const =0

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

Protected Attributes
Scalar	mu_ = 0.

Scalar	mu_inv_

Detailed Description

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

Base constraint set type.

Constraint sets can be the negative or positive orthant, the \(\{0\}\) singleton, cones, etc... The expected inputs are constraint values or shifted constraint values (as in ALM-type algorithms).

Definition at line 16 of file constraint-set.hpp.

Member Typedef Documentation

◆ Scalar

template<typename _Scalar>

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

Definition at line 18 of file constraint-set.hpp.

◆ ActiveType

template<typename _Scalar>

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

Definition at line 20 of file constraint-set.hpp.

Constructor & Destructor Documentation

◆ ConstraintSetTpl()

template<typename _Scalar>

aligator::ConstraintSetTpl< _Scalar >::ConstraintSetTpl ( )

default

◆ ~ConstraintSetTpl()

template<typename _Scalar>

virtual aligator::ConstraintSetTpl< _Scalar >::~ConstraintSetTpl ( )

virtualdefault

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

template<typename _Scalar>

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

◆ disableGaussNewton()

template<typename _Scalar>

virtual bool aligator::ConstraintSetTpl< _Scalar >::disableGaussNewton ( ) const

inlinevirtual

Do not use the vector-Hessian product in the Hessian for Gauss Newton.

Reimplemented in aligator::EqualityConstraintTpl< _Scalar >, aligator::EqualityConstraintTpl< Scalar >, and aligator::EqualityConstraintTpl< Scalar >.

Definition at line 26 of file constraint-set.hpp.

◆ evaluate()

template<typename _Scalar>

virtual Scalar aligator::ConstraintSetTpl< _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 in aligator::ConstraintSetProductTpl< Scalar >, aligator::NonsmoothPenaltyL1Tpl< _Scalar >, aligator::NonsmoothPenaltyL1Tpl< Scalar >, and aligator::NonsmoothPenaltyL1Tpl< Scalar >.

Definition at line 31 of file constraint-set.hpp.

◆ projection()

template<typename _Scalar>

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

pure virtual

Compute projection of variable z onto the constraint set.

Parameters

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

Implemented in aligator::BoxConstraintTpl< Scalar >, aligator::ConstraintSetProductTpl< Scalar >, aligator::EqualityConstraintTpl< _Scalar >, aligator::EqualityConstraintTpl< Scalar >, aligator::EqualityConstraintTpl< Scalar >, aligator::NegativeOrthantTpl< _Scalar >, aligator::NegativeOrthantTpl< Scalar >, aligator::NegativeOrthantTpl< Scalar >, aligator::NonsmoothPenaltyL1Tpl< _Scalar >, aligator::NonsmoothPenaltyL1Tpl< Scalar >, and aligator::NonsmoothPenaltyL1Tpl< Scalar >.

◆ normalConeProjection()

template<typename _Scalar>

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

pure virtual

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

Implemented in aligator::BoxConstraintTpl< Scalar >, aligator::ConstraintSetProductTpl< Scalar >, aligator::EqualityConstraintTpl< _Scalar >, aligator::EqualityConstraintTpl< Scalar >, aligator::EqualityConstraintTpl< Scalar >, aligator::NegativeOrthantTpl< _Scalar >, aligator::NegativeOrthantTpl< Scalar >, aligator::NegativeOrthantTpl< Scalar >, aligator::NonsmoothPenaltyL1Tpl< _Scalar >, aligator::NonsmoothPenaltyL1Tpl< Scalar >, and aligator::NonsmoothPenaltyL1Tpl< Scalar >.

◆ applyProjectionJacobian()

template<typename _Scalar>

virtual void aligator::ConstraintSetTpl< _Scalar >::applyProjectionJacobian	(	const ConstVectorRef &	z,
		MatrixRef	Jout ) const

virtual

Apply a jacobian of the projection/proximal operator to a matrix.

This carries out the product \(PJ\), where \( P \in\partial_B\prox(z)\).

Parameters

[in]	z	Input vector (multiplier estimate)
[out]	Jout	Output Jacobian matrix, which will be modifed in-place and returned.

Reimplemented in aligator::ConstraintSetProductTpl< Scalar >, aligator::EqualityConstraintTpl< _Scalar >, aligator::EqualityConstraintTpl< Scalar >, and aligator::EqualityConstraintTpl< Scalar >.

◆ applyNormalConeProjectionJacobian()

template<typename _Scalar>

virtual void aligator::ConstraintSetTpl< _Scalar >::applyNormalConeProjectionJacobian	(	const ConstVectorRef &	z,
		MatrixRef	Jout ) const

virtual

Apply the jacobian of the projection on the normal cone.

Parameters

[in]	z	Input vector
[out]	Jout	Output Jacobian matrix of shape \((nr, ndx)\), which will be modified in place. The modification should be a row-wise operation.

Reimplemented in aligator::ConstraintSetProductTpl< Scalar >, aligator::EqualityConstraintTpl< _Scalar >, aligator::EqualityConstraintTpl< Scalar >, and aligator::EqualityConstraintTpl< Scalar >.

◆ setProxParameter()

template<typename _Scalar>

void aligator::ConstraintSetTpl< _Scalar >::setProxParameter ( const Scalar mu ) const

inline

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

Definition at line 68 of file constraint-set.hpp.

◆ computeActiveSet()

template<typename _Scalar>

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

pure virtual

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

Implemented in aligator::BoxConstraintTpl< Scalar >, aligator::ConstraintSetProductTpl< Scalar >, aligator::EqualityConstraintTpl< _Scalar >, aligator::EqualityConstraintTpl< Scalar >, aligator::EqualityConstraintTpl< Scalar >, aligator::NegativeOrthantTpl< _Scalar >, aligator::NegativeOrthantTpl< Scalar >, aligator::NegativeOrthantTpl< Scalar >, aligator::NonsmoothPenaltyL1Tpl< _Scalar >, aligator::NonsmoothPenaltyL1Tpl< Scalar >, and aligator::NonsmoothPenaltyL1Tpl< Scalar >.

◆ operator==()

template<typename _Scalar>

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

inline

Definition at line 80 of file constraint-set.hpp.

◆ evaluateMoreauEnvelope()

template<typename _Scalar>

Scalar aligator::ConstraintSetTpl< _Scalar >::evaluateMoreauEnvelope	(	const ConstVectorRef &	zin,
		const ConstVectorRef &	zproj ) const

inline

Evaluate the Moreau envelope with parameter mu for the given contraint set or nonsmooth penalty \(g\) at point zin.

The envelope is

\[ M_{\mu g}(z) := g(\prox_{\mu g}(z)) + \frac{1}{2\mu} \| z - \prox_{\mu g}(z) \|^2. \]

Parameters

zin	The input.
zproj	Projection of the input to the normal.

Definition at line 93 of file constraint-set.hpp.

◆ computeMoreauEnvelope()

template<typename _Scalar>

Scalar aligator::ConstraintSetTpl< _Scalar >::computeMoreauEnvelope	(	const ConstVectorRef &	zin,
		VectorRef	zprojout ) const

inline

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.

The envelope is

\[ M_{\mu g}(z) := g(\prox_{\mu g}(z)) + \frac{1}{2\mu} \| z - \prox_{\mu g}(z) \|^2. \]

Parameters

zin	The input.
zproj	Projection of the input to the normal.

Definition at line 102 of file constraint-set.hpp.

◆ mu()

template<typename _Scalar>

Scalar aligator::ConstraintSetTpl< _Scalar >::mu ( ) const

inline

Definition at line 108 of file constraint-set.hpp.

◆ mu_inv()

template<typename _Scalar>

Scalar aligator::ConstraintSetTpl< _Scalar >::mu_inv ( ) const

inline

Definition at line 109 of file constraint-set.hpp.

Member Data Documentation

◆ mu_

template<typename _Scalar>

Scalar aligator::ConstraintSetTpl< _Scalar >::mu_ = 0.

mutableprotected

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

◆ mu_inv_

template<typename _Scalar>

Scalar aligator::ConstraintSetTpl< _Scalar >::mu_inv_

mutableprotected

Definition at line 113 of file constraint-set.hpp.

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

include/aligator/core/constraint-set.hpp

Public Types

Public Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Scalar

◆ ActiveType

Constructor & Destructor Documentation

◆ ConstraintSetTpl()

◆ ~ConstraintSetTpl()

Member Function Documentation

◆ ALIGATOR_DYNAMIC_TYPEDEFS()

◆ disableGaussNewton()

◆ evaluate()

◆ projection()

◆ normalConeProjection()

◆ applyProjectionJacobian()

◆ applyNormalConeProjectionJacobian()

◆ setProxParameter()

◆ computeActiveSet()

◆ operator==()

◆ evaluateMoreauEnvelope()

◆ computeMoreauEnvelope()

◆ mu()

◆ mu_inv()

Member Data Documentation

◆ mu_

◆ mu_inv_