ROL
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ROL::QuadraticPenalty< Real > Class Template Reference

Provides the interface to evaluate the quadratic constraint penalty. More...

#include <ROL_QuadraticPenalty.hpp>

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

Public Member Functions

 QuadraticPenalty (const ROL::Ptr< Constraint< Real > > &con, const Vector< Real > &multiplier, const Real penaltyParameter, const Vector< Real > &optVec, const Vector< Real > &conVec, const bool useScaling=false, const int HessianApprox=0)
 
void setScaling (const Real cscale=1)
 
virtual void update (const Vector< Real > &x, bool flag=true, int iter=-1)
 Update objective function. More...
 
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 void getConstraintVec (Vector< Real > &c, const Vector< Real > &x)
 
virtual int getNumberConstraintEvaluations (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 Member Functions

void evaluateConstraint (const Vector< Real > &x, Real &tol)
 

Private Attributes

const ROL::Ptr< Constraint
< Real > > 
con_
 
ROL::Ptr< Vector< Real > > multiplier_
 
Real penaltyParameter_
 
ROL::Ptr< Vector< Real > > primalMultiplierVector_
 
ROL::Ptr< Vector< Real > > dualOptVector_
 
ROL::Ptr< Vector< Real > > primalConVector_
 
ROL::Ptr< Vector< Real > > conValue_
 
Real cscale_
 
int ncval_
 
const bool useScaling_
 
const int HessianApprox_
 
bool isConstraintComputed_
 

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::QuadraticPenalty< Real >

Provides the interface to evaluate the quadratic constraint penalty.

This class implements the quadratic constraint penalty functional. Given an equality constraint \(c:\mathcal{X}\to\mathcal{C}\), the quadratic penalty functional is

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

where \(\lambda\in\mathcal{C}^*\) denotes a multiplier, \(\mu > 0\) 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 \(Q\) by \(\mu^{-1}\) and also permits the Hessian approximation

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


Definition at line 50 of file ROL_QuadraticPenalty.hpp.

Constructor & Destructor Documentation

template<class Real >
ROL::QuadraticPenalty< Real >::QuadraticPenalty ( const ROL::Ptr< Constraint< Real > > &  con,
const Vector< Real > &  multiplier,
const Real  penaltyParameter,
const Vector< Real > &  optVec,
const Vector< Real > &  conVec,
const bool  useScaling = false,
const int  HessianApprox = 0 
)
inline

Member Function Documentation

template<class Real >
void ROL::QuadraticPenalty< Real >::evaluateConstraint ( const Vector< Real > &  x,
Real &  tol 
)
inlineprivate
template<class Real >
void ROL::QuadraticPenalty< Real >::setScaling ( const Real  cscale = 1)
inline

Definition at line 102 of file ROL_QuadraticPenalty.hpp.

References ROL::QuadraticPenalty< Real >::cscale_.

template<class Real >
virtual void ROL::QuadraticPenalty< 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 >.

Definition at line 106 of file ROL_QuadraticPenalty.hpp.

References ROL::QuadraticPenalty< Real >::con_, and ROL::QuadraticPenalty< Real >::isConstraintComputed_.

template<class Real >
virtual Real ROL::QuadraticPenalty< Real >::value ( const Vector< Real > &  x,
Real &  tol 
)
inlinevirtual

Compute value.

This function returns the objective function value.

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

Implements ROL::Objective< Real >.

Definition at line 111 of file ROL_QuadraticPenalty.hpp.

References ROL::QuadraticPenalty< Real >::conValue_, ROL::QuadraticPenalty< Real >::cscale_, ROL::QuadraticPenalty< Real >::evaluateConstraint(), ROL::QuadraticPenalty< Real >::multiplier_, ROL::QuadraticPenalty< Real >::penaltyParameter_, and ROL::QuadraticPenalty< Real >::useScaling_.

template<class Real >
virtual void ROL::QuadraticPenalty< 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 130 of file ROL_QuadraticPenalty.hpp.

References ROL::QuadraticPenalty< Real >::con_, ROL::QuadraticPenalty< Real >::conValue_, ROL::QuadraticPenalty< Real >::cscale_, ROL::QuadraticPenalty< Real >::evaluateConstraint(), ROL::QuadraticPenalty< Real >::multiplier_, ROL::QuadraticPenalty< Real >::penaltyParameter_, ROL::QuadraticPenalty< Real >::primalMultiplierVector_, and ROL::QuadraticPenalty< Real >::useScaling_.

template<class Real >
virtual void ROL::QuadraticPenalty< Real >::hessVec ( Vector< Real > &  hv,
const Vector< Real > &  v,
const Vector< Real > &  x,
Real &  tol 
)
inlinevirtual
template<class Real >
virtual void ROL::QuadraticPenalty< Real >::getConstraintVec ( Vector< Real > &  c,
const Vector< Real > &  x 
)
inlinevirtual
template<class Real >
virtual int ROL::QuadraticPenalty< Real >::getNumberConstraintEvaluations ( void  ) const
inlinevirtual

Definition at line 203 of file ROL_QuadraticPenalty.hpp.

References ROL::QuadraticPenalty< Real >::ncval_.

template<class Real >
virtual void ROL::QuadraticPenalty< Real >::reset ( const Vector< Real > &  multiplier,
const Real  penaltyParameter 
)
inlinevirtual

Member Data Documentation

template<class Real >
const ROL::Ptr<Constraint<Real> > ROL::QuadraticPenalty< Real >::con_
private
template<class Real >
ROL::Ptr<Vector<Real> > ROL::QuadraticPenalty< Real >::multiplier_
private
template<class Real >
Real ROL::QuadraticPenalty< Real >::penaltyParameter_
private
template<class Real >
ROL::Ptr<Vector<Real> > ROL::QuadraticPenalty< Real >::primalMultiplierVector_
private
template<class Real >
ROL::Ptr<Vector<Real> > ROL::QuadraticPenalty< Real >::dualOptVector_
private
template<class Real >
ROL::Ptr<Vector<Real> > ROL::QuadraticPenalty< Real >::primalConVector_
private
template<class Real >
ROL::Ptr<Vector<Real> > ROL::QuadraticPenalty< Real >::conValue_
private
template<class Real >
Real ROL::QuadraticPenalty< Real >::cscale_
private
template<class Real >
int ROL::QuadraticPenalty< Real >::ncval_
private
template<class Real >
const bool ROL::QuadraticPenalty< Real >::useScaling_
private
template<class Real >
const int ROL::QuadraticPenalty< Real >::HessianApprox_
private

Definition at line 71 of file ROL_QuadraticPenalty.hpp.

Referenced by ROL::QuadraticPenalty< Real >::hessVec().

template<class Real >
bool ROL::QuadraticPenalty< Real >::isConstraintComputed_
private

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