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)
	Compute the proximity operator. More...

virtual void	proxJacVec (Vector< Real > &Jv, const Vector< Real > &v, const Vector< Real > &x, Real t, Real &tol)
	Apply the Jacobian of the proximity operator. More...

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 std::vector < std::vector< Real > >	checkProxJacVec (const Vector< Real > &x, const Vector< Real > &v, Real t=Real(1), bool printToStream=true, std::ostream &outStream=std::cout, int numSteps=ROL_NUM_CHECKDERIV_STEPS)
	Finite-difference proximity operator Jacobian-applied-to-vector 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

Definition at line 85 of file ROL_QuadraticPenalty.hpp.

References ROL::Vector< Real >::clone(), ROL::QuadraticPenalty< Real >::conValue_, ROL::Vector< Real >::dual(), ROL::QuadraticPenalty< Real >::dualOptVector_, ROL::QuadraticPenalty< Real >::multiplier_, ROL::QuadraticPenalty< Real >::primalConVector_, and ROL::QuadraticPenalty< Real >::primalMultiplierVector_.

Member Function Documentation

template<class Real >

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

inlineprivate

Definition at line 76 of file ROL_QuadraticPenalty.hpp.

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

Referenced by ROL::QuadraticPenalty< Real >::getConstraintVec(), ROL::QuadraticPenalty< Real >::gradient(), ROL::QuadraticPenalty< Real >::hessVec(), and ROL::QuadraticPenalty< Real >::value().

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]	x	is the new iterate.
[in]	flag	is true if the iterate has changed.
[in]	iter	is 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]	x	is the current iterate.
[in]	tol	is 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]	g	is the gradient.
[in]	x	is the current iterate.
[in]	tol	is 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

Apply Hessian approximation to vector.

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

Parameters

[out]	hv	is the the action of the Hessian on \(v\).
[in]	v	is the direction vector.
[in]	x	is the current iterate.
[in]	tol	is a tolerance for inexact objective function computation.