ROL
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ROL::AugmentedLagrangianObjective< Real > Class Template Reference

Provides the interface to evaluate the augmented Lagrangian. More...

#include <ROL_AugmentedLagrangianObjective.hpp>

+ Inheritance diagram for ROL::AugmentedLagrangianObjective< Real >:

Public Member Functions

 AugmentedLagrangianObjective (const Ptr< Objective< Real >> &obj, const Ptr< Constraint< Real >> &con, const Real penaltyParameter, const Vector< Real > &dualOptVec, const Vector< Real > &primConVec, const Vector< Real > &dualConVec, ParameterList &parlist)
 
 AugmentedLagrangianObjective (const Ptr< Objective< Real >> &obj, const Ptr< Constraint< Real >> &con, const Real penaltyParameter, const Vector< Real > &dualOptVec, const Vector< Real > &primConVec, const Vector< Real > &dualConVec, const bool scaleLagrangian, const int HessianApprox)
 
void update (const Vector< Real > &x, UpdateType type, int iter=-1)
 Update objective function. More...
 
void setScaling (const Real fscale=1.0, const Real cscale=1.0)
 
Real value (const Vector< Real > &x, Real &tol)
 Compute value. More...
 
void gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol)
 Compute gradient. More...
 
void hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
 Apply Hessian approximation to vector. More...
 
Real getObjectiveValue (const Vector< Real > &x, Real &tol)
 
const Ptr< const Vector< Real > > getObjectiveGradient (const Vector< Real > &x, Real &tol)
 
const Ptr< const Vector< Real > > getConstraintVec (const Vector< Real > &x, Real &tol)
 
int getNumberConstraintEvaluations (void) const
 
int getNumberFunctionEvaluations (void) const
 
int getNumberGradientEvaluations (void) const
 
void reset (const Vector< Real > &multiplier, const Real penaltyParameter)
 
- Public Member Functions inherited from ROL::Objective< Real >
virtual ~Objective ()
 
 Objective ()
 
virtual void update (const Vector< Real > &x, bool flag=true, int iter=-1)
 Update objective function. More...
 
virtual Real dirDeriv (const Vector< Real > &x, const Vector< Real > &d, Real &tol)
 Compute directional derivative. More...
 
virtual void invHessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
 Apply inverse Hessian approximation to vector. More...
 
virtual void precond (Vector< Real > &Pv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
 Apply preconditioner to vector. More...
 
virtual void prox (Vector< Real > &Pv, const Vector< Real > &v, Real t, Real &tol)
 
virtual std::vector
< std::vector< Real > > 
checkGradient (const Vector< Real > &x, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
 Finite-difference gradient check. More...
 
virtual std::vector
< std::vector< Real > > 
checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
 Finite-difference gradient check. More...
 
virtual std::vector
< std::vector< Real > > 
checkGradient (const Vector< Real > &x, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
 Finite-difference gradient check with specified step sizes. More...
 
virtual std::vector
< std::vector< Real > > 
checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
 Finite-difference gradient check with specified step sizes. More...
 
virtual std::vector
< std::vector< Real > > 
checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
 Finite-difference Hessian-applied-to-vector check. More...
 
virtual std::vector
< std::vector< Real > > 
checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
 Finite-difference Hessian-applied-to-vector check. More...
 
virtual std::vector
< std::vector< Real > > 
checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
 Finite-difference Hessian-applied-to-vector check with specified step sizes. More...
 
virtual std::vector
< std::vector< Real > > 
checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
 Finite-difference Hessian-applied-to-vector check with specified step sizes. More...
 
virtual std::vector< Real > checkHessSym (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout)
 Hessian symmetry check. More...
 
virtual std::vector< Real > checkHessSym (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout)
 Hessian symmetry check. More...
 
virtual void setParameter (const std::vector< Real > &param)
 

Private Attributes

const Ptr< Objective< Real > > obj_
 
const Ptr< Constraint< Real > > con_
 
Real penaltyParameter_
 
Ptr< Vector< Real > > multiplier_
 
Ptr< Vector< Real > > dualOptVector_
 
Ptr< Vector< Real > > dualConVector_
 
Ptr< Vector< Real > > primConVector_
 
Ptr< ScalarController< Real,
int > > 
fval_
 
Ptr< VectorController< Real,
int > > 
gradient_
 
Ptr< VectorController< Real,
int > > 
conValue_
 
Real fscale_
 
Real cscale_
 
int nfval_
 
int ngval_
 
int ncval_
 
bool scaleLagrangian_
 
int HessianApprox_
 

Additional Inherited Members

- Protected Member Functions inherited from ROL::Objective< Real >
const std::vector< Real > getParameter (void) const
 

Detailed Description

template<class Real>
class ROL::AugmentedLagrangianObjective< Real >

Provides the interface to evaluate the augmented Lagrangian.

This class implements the augmented Lagrangian functional for use with ROL::AugmentedLagrangianAlgorithm. Given a function \(f:\mathcal{X}\to\mathbb{R}\) and an equality constraint \(c:\mathcal{X}\to\mathcal{C}\), the augmented Lagrangian functional is

\[ L_A(x,\lambda,\mu) = f(x) + \langle \lambda, c(x)\rangle_{\mathcal{C}^*,\mathcal{C}} + \frac{\mu}{2} \langle \mathfrak{R}c(x),c(x)\rangle_{\mathcal{C}^*,\mathcal{C}} \]

where \(\lambda\in\mathcal{C}^*\) denotes the Lagrange multiplier estimate, \(\mu > 0\) is the penalty parameter and \(\mathfrak{R}\in\mathcal{L}(\mathcal{C},\mathcal{C}^*)\) is the Riesz operator on the constraint space.

This implementation permits the scaling of \(L_A\) by \(\mu^{-1}\) and also permits the Hessian approximation

\[ \nabla^2_x L_A(x,\lambda,\mu)v \approx \nabla^2 f(x) v + \mu c'(x)^*\mathfrak{R} c'(x)v. \]


Definition at line 54 of file ROL_AugmentedLagrangianObjective.hpp.

Constructor & Destructor Documentation

template<class Real>
ROL::AugmentedLagrangianObjective< Real >::AugmentedLagrangianObjective ( const Ptr< Objective< Real >> &  obj,
const Ptr< Constraint< Real >> &  con,
const Real  penaltyParameter,
const Vector< Real > &  dualOptVec,
const Vector< Real > &  primConVec,
const Vector< Real > &  dualConVec,
ParameterList &  parlist 
)
inline
template<class Real>
ROL::AugmentedLagrangianObjective< Real >::AugmentedLagrangianObjective ( const Ptr< Objective< Real >> &  obj,
const Ptr< Constraint< Real >> &  con,
const Real  penaltyParameter,
const Vector< Real > &  dualOptVec,
const Vector< Real > &  primConVec,
const Vector< Real > &  dualConVec,
const bool  scaleLagrangian,
const int  HessianApprox 
)
inline

Member Function Documentation

template<class Real>
void ROL::AugmentedLagrangianObjective< Real >::update ( const Vector< Real > &  x,
UpdateType  type,
int  iter = -1 
)
inlinevirtual

Update objective function.

This function updates the objective function at new iterations.

Parameters
[in]xis the new iterate.
[in]typeis the type of update requested.
[in]iteris the outer algorithm iterations count.

Reimplemented from ROL::Objective< Real >.

Definition at line 133 of file ROL_AugmentedLagrangianObjective.hpp.

References ROL::AugmentedLagrangianObjective< Real >::con_, ROL::AugmentedLagrangianObjective< Real >::conValue_, ROL::AugmentedLagrangianObjective< Real >::fval_, ROL::AugmentedLagrangianObjective< Real >::gradient_, and ROL::AugmentedLagrangianObjective< Real >::obj_.

Referenced by ROL::TypeE::AugmentedLagrangianAlgorithm< Real >::initialize(), and ROL::TypeG::AugmentedLagrangianAlgorithm< Real >::initialize().

template<class Real>
void ROL::AugmentedLagrangianObjective< Real >::setScaling ( const Real  fscale = 1.0,
const Real  cscale = 1.0 
)
inline
template<class Real>
Real ROL::AugmentedLagrangianObjective< Real >::value ( const Vector< Real > &  x,
Real &  tol 
)
inlinevirtual
template<class Real>
void ROL::AugmentedLagrangianObjective< Real >::gradient ( Vector< Real > &  g,
const Vector< Real > &  x,
Real &  tol 
)
inlinevirtual

Compute gradient.

This function returns the objective function gradient.

Parameters
[out]gis the gradient.
[in]xis the current iterate.
[in]tolis a tolerance for inexact objective function computation.

The default implementation is a finite-difference approximation based on the function value. This requires the definition of a basis \(\{\phi_i\}\) for the optimization vectors x and the definition of a basis \(\{\psi_j\}\) for the dual optimization vectors (gradient vectors g). The bases must be related through the Riesz map, i.e., \( R \{\phi_i\} = \{\psi_j\}\), and this must be reflected in the implementation of the ROL::Vector::dual() method.

Reimplemented from ROL::Objective< Real >.

Definition at line 162 of file ROL_AugmentedLagrangianObjective.hpp.

References ROL::Vector< Real >::axpy(), ROL::AugmentedLagrangianObjective< Real >::con_, ROL::AugmentedLagrangianObjective< Real >::cscale_, ROL::AugmentedLagrangianObjective< Real >::dualConVector_, ROL::AugmentedLagrangianObjective< Real >::dualOptVector_, ROL::AugmentedLagrangianObjective< Real >::fscale_, ROL::AugmentedLagrangianObjective< Real >::getConstraintVec(), ROL::AugmentedLagrangianObjective< Real >::getObjectiveGradient(), ROL::AugmentedLagrangianObjective< Real >::multiplier_, ROL::AugmentedLagrangianObjective< Real >::penaltyParameter_, ROL::Vector< Real >::scale(), ROL::AugmentedLagrangianObjective< Real >::scaleLagrangian_, and ROL::Vector< Real >::set().

Referenced by ROL::TypeE::AugmentedLagrangianAlgorithm< Real >::initialize(), ROL::TypeG::AugmentedLagrangianAlgorithm< Real >::initialize(), ROL::TypeE::AugmentedLagrangianAlgorithm< Real >::run(), and ROL::TypeG::AugmentedLagrangianAlgorithm< Real >::run().

template<class Real>
void ROL::AugmentedLagrangianObjective< Real >::hessVec ( Vector< Real > &  hv,
const Vector< Real > &  v,
const Vector< Real > &  x,
Real &  tol 
)
inlinevirtual
template<class Real>
Real ROL::AugmentedLagrangianObjective< Real >::getObjectiveValue ( const Vector< Real > &  x,
Real &  tol 
)
inline
template<class Real>
const Ptr<const Vector<Real> > ROL::AugmentedLagrangianObjective< Real >::getObjectiveGradient ( const Vector< Real > &  x,
Real &  tol 
)
inline
template<class Real>
const Ptr<const Vector<Real> > ROL::AugmentedLagrangianObjective< Real >::getConstraintVec ( const Vector< Real > &  x,
Real &  tol 
)
inline
template<class Real>
int ROL::AugmentedLagrangianObjective< Real >::getNumberConstraintEvaluations ( void  ) const
inline
template<class Real>
int ROL::AugmentedLagrangianObjective< Real >::getNumberFunctionEvaluations ( void  ) const
inline
template<class Real>
int ROL::AugmentedLagrangianObjective< Real >::getNumberGradientEvaluations ( void  ) const
inline
template<class Real>
void ROL::AugmentedLagrangianObjective< Real >::reset ( const Vector< Real > &  multiplier,
const Real  penaltyParameter 
)
inline

Member Data Documentation

template<class Real>
const Ptr<Objective<Real> > ROL::AugmentedLagrangianObjective< Real >::obj_
private
template<class Real>
const Ptr<Constraint<Real> > ROL::AugmentedLagrangianObjective< Real >::con_
private
template<class Real>
Real ROL::AugmentedLagrangianObjective< Real >::penaltyParameter_
private
template<class Real>
Ptr<Vector<Real> > ROL::AugmentedLagrangianObjective< Real >::multiplier_
private
template<class Real>
Ptr<Vector<Real> > ROL::AugmentedLagrangianObjective< Real >::dualOptVector_
private
template<class Real>
Ptr<Vector<Real> > ROL::AugmentedLagrangianObjective< Real >::dualConVector_
private
template<class Real>
Ptr<Vector<Real> > ROL::AugmentedLagrangianObjective< Real >::primConVector_
private
template<class Real>
Ptr<ScalarController<Real,int> > ROL::AugmentedLagrangianObjective< Real >::fval_
private
template<class Real>
Ptr<VectorController<Real,int> > ROL::AugmentedLagrangianObjective< Real >::gradient_
private
template<class Real>
Ptr<VectorController<Real,int> > ROL::AugmentedLagrangianObjective< Real >::conValue_
private
template<class Real>
Real ROL::AugmentedLagrangianObjective< Real >::fscale_
private
template<class Real>
Real ROL::AugmentedLagrangianObjective< Real >::cscale_
private
template<class Real>
int ROL::AugmentedLagrangianObjective< Real >::nfval_
private
template<class Real>
int ROL::AugmentedLagrangianObjective< Real >::ngval_
private
template<class Real>
int ROL::AugmentedLagrangianObjective< Real >::ncval_
private
template<class Real>
bool ROL::AugmentedLagrangianObjective< Real >::scaleLagrangian_
private
template<class Real>
int ROL::AugmentedLagrangianObjective< Real >::HessianApprox_
private

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