ROL
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ROL::AugmentedLagrangian< Real > Class Template Reference

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

#include <ROL_AugmentedLagrangian.hpp>

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

Public Member Functions

 AugmentedLagrangian (const ROL::Ptr< Objective< Real > > &obj, const ROL::Ptr< Constraint< Real > > &con, const Vector< Real > &multiplier, const Real penaltyParameter, const Vector< Real > &optVec, const Vector< Real > &conVec, ROL::ParameterList &parlist)
 Constructor. More...
 
 AugmentedLagrangian (const ROL::Ptr< Objective< Real > > &obj, const ROL::Ptr< Constraint< Real > > &con, const Vector< Real > &multiplier, const Real penaltyParameter, const Vector< Real > &optVec, const Vector< Real > &conVec, const bool scaleLagrangian, const int HessianApprox)
 Constructor. More...
 
 AugmentedLagrangian ()
 Null constructor. More...
 
virtual void update (const Vector< Real > &x, bool flag=true, int iter=-1)
 Update objective function. More...
 
void setScaling (const Real fscale, const Real cscale=1.0)
 
virtual Real value (const Vector< Real > &x, Real &tol)
 Compute value. More...
 
virtual void gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol)
 Compute gradient. More...
 
virtual void hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
 Apply Hessian approximation to vector. More...
 
virtual Real getObjectiveValue (const Vector< Real > &x)
 
const Ptr< const Vector< Real > > getObjectiveGradient (const Vector< Real > &x)
 
virtual void getConstraintVec (Vector< Real > &c, const Vector< Real > &x)
 
virtual int getNumberConstraintEvaluations (void) const
 
virtual int getNumberFunctionEvaluations (void) const
 
virtual int getNumberGradientEvaluations (void) const
 
virtual 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, UpdateType type, 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 ROL::Ptr< Objective< Real > > obj_
 
ROL::Ptr< QuadraticPenalty
< Real > > 
pen_
 
Real penaltyParameter_
 
ROL::Ptr< Vector< Real > > dualOptVector_
 
Real fval_
 
ROL::Ptr< Vector< Real > > gradient_
 
Real fscale_
 
int nfval_
 
int ngval_
 
bool scaleLagrangian_
 
bool isValueComputed_
 
bool isGradientComputed_
 

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::AugmentedLagrangian< Real >

Provides the interface to evaluate the augmented Lagrangian.

This class implements the augmented Lagrangian functional for use with ROL::AugmentedLagrangianStep. 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 52 of file ROL_AugmentedLagrangian.hpp.

Constructor & Destructor Documentation

template<class Real>
ROL::AugmentedLagrangian< Real >::AugmentedLagrangian ( const ROL::Ptr< Objective< Real > > &  obj,
const ROL::Ptr< Constraint< Real > > &  con,
const Vector< Real > &  multiplier,
const Real  penaltyParameter,
const Vector< Real > &  optVec,
const Vector< Real > &  conVec,
ROL::ParameterList &  parlist 
)
inline

Constructor.

This creates a valid AugmentedLagrangian object.

Parameters
[in]objis an objective function.
[in]conis an equality constraint.
[in]mulitplieris a Lagrange multiplier vector.
[in]penaltyParameteris the penalty parameter.
[in]optVecis an optimization space vector.
[in]conVecis a constraint space vector.
[in]parlistis a parameter list.

Definition at line 92 of file ROL_AugmentedLagrangian.hpp.

References ROL::Vector< Real >::dual(), ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::gradient_, ROL::AugmentedLagrangian< Real >::pen_, and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.

template<class Real>
ROL::AugmentedLagrangian< Real >::AugmentedLagrangian ( const ROL::Ptr< Objective< Real > > &  obj,
const ROL::Ptr< Constraint< Real > > &  con,
const Vector< Real > &  multiplier,
const Real  penaltyParameter,
const Vector< Real > &  optVec,
const Vector< Real > &  conVec,
const bool  scaleLagrangian,
const int  HessianApprox 
)
inline

Constructor.

This creates a valid AugmentedLagrangian object.

Parameters
[in]objis an objective function.
[in]conis an equality constraint.
[in]mulitplieris a Lagrange multiplier vector.
[in]penaltyParameteris the penalty parameter.
[in]optVecis an optimization space vector.
[in]conVecis a constraint space vector.
[in]parlistis a parameter list.

Definition at line 125 of file ROL_AugmentedLagrangian.hpp.

References ROL::Vector< Real >::dual(), ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::gradient_, ROL::AugmentedLagrangian< Real >::pen_, and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.

template<class Real>
ROL::AugmentedLagrangian< Real >::AugmentedLagrangian ( )
inline

Null constructor.

This constructor is only used for inheritance and does not create a valid AugmentedLagrangian object. Do not use.

Definition at line 150 of file ROL_AugmentedLagrangian.hpp.

Member Function Documentation

template<class Real>
virtual void ROL::AugmentedLagrangian< Real >::update ( const Vector< Real > &  x,
bool  flag = true,
int  iter = -1 
)
inlinevirtual

Update objective function.

This function updates the objective function at new iterations.

Parameters
[in]xis the new iterate.
[in]flagis true if the iterate has changed.
[in]iteris the outer algorithm iterations count.

Reimplemented from ROL::Objective< Real >.

Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.

Definition at line 156 of file ROL_AugmentedLagrangian.hpp.

References ROL::AugmentedLagrangian< Real >::isGradientComputed_, ROL::AugmentedLagrangian< Real >::isValueComputed_, ROL::AugmentedLagrangian< Real >::obj_, and ROL::AugmentedLagrangian< Real >::pen_.

Referenced by ROL::AugmentedLagrangianStep< Real >::initialize(), and ROL::AugmentedLagrangianStep< Real >::update().

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

Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.

Definition at line 184 of file ROL_AugmentedLagrangian.hpp.

References ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::fscale_, ROL::AugmentedLagrangian< Real >::gradient_, ROL::AugmentedLagrangian< Real >::isGradientComputed_, ROL::AugmentedLagrangian< Real >::ngval_, ROL::AugmentedLagrangian< Real >::obj_, ROL::AugmentedLagrangian< Real >::pen_, ROL::AugmentedLagrangian< Real >::penaltyParameter_, ROL::Vector< Real >::plus(), ROL::Vector< Real >::scale(), ROL::AugmentedLagrangian< Real >::scaleLagrangian_, and ROL::Vector< Real >::set().

Referenced by ROL::AugmentedLagrangianStep< Real >::computeGradient().

template<class Real>
virtual void ROL::AugmentedLagrangian< Real >::hessVec ( Vector< Real > &  hv,
const Vector< Real > &  v,
const Vector< Real > &  x,
Real &  tol 
)
inlinevirtual

Apply Hessian approximation to vector.

This function applies the Hessian of the objective function to the vector \(v\).

Parameters
[out]hvis the the action of the Hessian on \(v\).
[in]vis the direction vector.
[in]xis the current iterate.
[in]tolis a tolerance for inexact objective function computation.

Reimplemented from ROL::Objective< Real >.

Reimplemented in ROL::Reduced_AugmentedLagrangian_SimOpt< Real >.

Definition at line 201 of file ROL_AugmentedLagrangian.hpp.

References ROL::AugmentedLagrangian< Real >::dualOptVector_, ROL::AugmentedLagrangian< Real >::fscale_, ROL::AugmentedLagrangian< Real >::obj_, ROL::AugmentedLagrangian< Real >::pen_, ROL::AugmentedLagrangian< Real >::penaltyParameter_, ROL::Vector< Real >::plus(), ROL::Vector< Real >::scale(), and ROL::AugmentedLagrangian< Real >::scaleLagrangian_.

template<class Real>
virtual Real ROL::AugmentedLagrangian< Real >::getObjectiveValue ( const Vector< Real > &  x)
inlinevirtual
template<class Real>
const Ptr<const Vector<Real> > ROL::AugmentedLagrangian< Real >::getObjectiveGradient ( const Vector< Real > &  x)
inline
template<class Real>
virtual void ROL::AugmentedLagrangian< Real >::getConstraintVec ( Vector< Real > &  c,
const Vector< Real > &  x 
)
inlinevirtual
template<class Real>
virtual int ROL::AugmentedLagrangian< Real >::getNumberConstraintEvaluations ( void  ) const
inlinevirtual
template<class Real>
virtual int ROL::AugmentedLagrangian< Real >::getNumberFunctionEvaluations ( void  ) const
inlinevirtual
template<class Real>
virtual int ROL::AugmentedLagrangian< Real >::getNumberGradientEvaluations ( void  ) const
inlinevirtual
template<class Real>
virtual void ROL::AugmentedLagrangian< Real >::reset ( const Vector< Real > &  multiplier,
const Real  penaltyParameter 
)
inlinevirtual

Member Data Documentation

template<class Real>
const ROL::Ptr<Objective<Real> > ROL::AugmentedLagrangian< Real >::obj_
private
template<class Real>
ROL::Ptr<QuadraticPenalty<Real> > ROL::AugmentedLagrangian< Real >::pen_
private
template<class Real>
Real ROL::AugmentedLagrangian< Real >::penaltyParameter_
private
template<class Real>
ROL::Ptr<Vector<Real> > ROL::AugmentedLagrangian< Real >::dualOptVector_
private
template<class Real>
Real ROL::AugmentedLagrangian< Real >::fval_
private
template<class Real>
ROL::Ptr<Vector<Real> > ROL::AugmentedLagrangian< Real >::gradient_
private
template<class Real>
Real ROL::AugmentedLagrangian< Real >::fscale_
private
template<class Real>
int ROL::AugmentedLagrangian< Real >::nfval_
private
template<class Real>
int ROL::AugmentedLagrangian< Real >::ngval_
private
template<class Real>
bool ROL::AugmentedLagrangian< Real >::scaleLagrangian_
private
template<class Real>
bool ROL::AugmentedLagrangian< Real >::isValueComputed_
private
template<class Real>
bool ROL::AugmentedLagrangian< Real >::isGradientComputed_
private

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