Composite \(\ell_1\)-penalty function \( \|c(x)\|_1 \). More...
#include <aligator/modelling/constraints/l1-penalty.hpp>
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
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
| using aligator::NonsmoothPenaltyL1Tpl< _Scalar >::Scalar = _Scalar |
Definition at line 19 of file l1-penalty.hpp.
◆ Base
| using aligator::NonsmoothPenaltyL1Tpl< _Scalar >::Base = ConstraintSetTpl<Scalar> |
Definition at line 28 of file l1-penalty.hpp.
◆ ActiveType
| using aligator::NonsmoothPenaltyL1Tpl< _Scalar >::ActiveType = typename Base::ActiveType |
Definition at line 29 of file l1-penalty.hpp.
Constructor & Destructor Documentation
◆ NonsmoothPenaltyL1Tpl() [1/3]
|
default |
◆ NonsmoothPenaltyL1Tpl() [2/3]
|
default |
◆ NonsmoothPenaltyL1Tpl() [3/3]
|
default |
Member Function Documentation
◆ ALIGATOR_DYNAMIC_TYPEDEFS()
| aligator::NonsmoothPenaltyL1Tpl< _Scalar >::ALIGATOR_DYNAMIC_TYPEDEFS | ( | Scalar | ) |
◆ operator=() [1/2]
|
default |
◆ operator=() [2/2]
|
default |
◆ evaluate()
|
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()
|
inline |
Definition at line 36 of file l1-penalty.hpp.
◆ projection()
|
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()
|
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()
|
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_
|
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
