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

#include <ROL_Reduced_AugmentedLagrangian_SimOpt.hpp>

Inheritance diagram for ROL::Reduced_AugmentedLagrangian_SimOpt< Real >:

Public Member Functions
	Reduced_AugmentedLagrangian_SimOpt (const ROL::Ptr< Objective_SimOpt< Real > > &obj, const ROL::Ptr< Constraint_SimOpt< Real > > &redCon, const ROL::Ptr< Constraint_SimOpt< Real > > &augCon, const ROL::Ptr< Vector< Real > > &state, const ROL::Ptr< Vector< Real > > &control, const ROL::Ptr< Vector< Real > > &adjoint, const ROL::Ptr< Vector< Real > > &augConVec, const ROL::Ptr< Vector< Real > > &multiplier, const Real penaltyParameter, ROL::ParameterList &parlist)

void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update objective function. More...

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)

void	getConstraintVec (Vector< Real > &c, const Vector< Real > &x)

int	getNumberConstraintEvaluations (void) const

int	getNumberFunctionEvaluations (void) const

int	getNumberGradientEvaluations (void) const

void	reset (const Vector< Real > &multiplier, const Real penaltyParameter)

void	setParameter (const std::vector< Real > &param)

Public Member Functions inherited from 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)
	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...

void	setScaling (const Real fscale, const Real cscale=1.0)

const Ptr< const Vector< Real > >	getObjectiveGradient (const Vector< Real > &x)

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...

Private Attributes
ROL::Ptr < AugmentedLagrangian_SimOpt < Real > >	augLagSimOpt_

ROL::Ptr < Reduced_Objective_SimOpt < Real > >	rAugLagSimOpt_

ROL::Ptr< Vector< Real > >	state_

int	ngval_

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::Reduced_AugmentedLagrangian_SimOpt< Real >

Provides the interface to evaluate the reduced SimOpt augmented Lagrangian.

This class implements the reduced SimOpt augmented Lagrangian functional for use with ROL::AugmentedLagrangianStep. Given a function \(f:\mathcal{U}\times\mathcal{Z}\to\mathbb{R}\), a reducible equality constaint \(c_r:\mathcal{U}\times\mathcal{Z}\to\mathcal{C}_r\) and another equality constraint \(c_a:\mathcal{U}\times\mathcal{Z}\to\mathcal{C}_a\), the (partially) augmented Lagrangian functional is

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

where \(\lambda\in\mathcal{C}_a^*\) denotes the Lagrange multiplier estimate, \(\mu > 0\) is the penalty parameter and \(\mathfrak{R}\in\mathcal{L}(\mathcal{C}_a,\mathcal{C}_a^*)\) is the Riesz operator on the constraint space \(\mathcal{C}_a\). Since \(c_r\) is reducible, there exists a solution operator \(S:\mathcal{Z}\to\mathcal{U}\) such that

\[ c_r(S(z),z) = 0 \quad\forall\, z\in\mathcal{Z}. \]

Substituting \(S(z)\) into \(L_A\) yields the reduced augmented Lagrangian \(\bar{L}_A(z,\lambda,\mu) = L_A(S(z),z,\lambda,\mu)\).

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

\[ \nabla^2_z \bar{L}_A(z,\lambda,\mu)v \approx \nabla^2 \bar{f}(z) v + \mu \bar{c}_a'(z)^*\mathfrak{R} \bar{c}_a'(z)v \]

where \(\bar{f}(z) = f(S(z),z)\) and \(\bar{c}_a(z) = c_a(S(z),z)\).

Definition at line 64 of file ROL_Reduced_AugmentedLagrangian_SimOpt.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::Reduced_AugmentedLagrangian_SimOpt< Real >::Reduced_AugmentedLagrangian_SimOpt	(	const ROL::Ptr< Objective_SimOpt< Real > > &	obj,
		const ROL::Ptr< Constraint_SimOpt< Real > > &	redCon,
		const ROL::Ptr< Constraint_SimOpt< Real > > &	augCon,
		const ROL::Ptr< Vector< Real > > &	state,
		const ROL::Ptr< Vector< Real > > &	control,
		const ROL::Ptr< Vector< Real > > &	adjoint,
		const ROL::Ptr< Vector< Real > > &	augConVec,
		const ROL::Ptr< Vector< Real > > &	multiplier,
		const Real	penaltyParameter,
		ROL::ParameterList &	parlist
	)

inline

Definition at line 74 of file ROL_Reduced_AugmentedLagrangian_SimOpt.hpp.

References ROL::Reduced_AugmentedLagrangian_SimOpt< Real >::augLagSimOpt_, and ROL::Reduced_AugmentedLagrangian_SimOpt< Real >::rAugLagSimOpt_.

Member Function Documentation

template<class Real >

void ROL::Reduced_AugmentedLagrangian_SimOpt< 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::AugmentedLagrangian< Real >.

Definition at line 100 of file ROL_Reduced_AugmentedLagrangian_SimOpt.hpp.

References ROL::Reduced_AugmentedLagrangian_SimOpt< Real >::rAugLagSimOpt_.

template<class Real >

Real ROL::Reduced_AugmentedLagrangian_SimOpt< 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.

Reimplemented from ROL::AugmentedLagrangian< Real >.

Definition at line 104 of file ROL_Reduced_AugmentedLagrangian_SimOpt.hpp.

References ROL::Reduced_AugmentedLagrangian_SimOpt< Real >::rAugLagSimOpt_.

template<class Real >

void ROL::Reduced_AugmentedLagrangian_SimOpt< 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::AugmentedLagrangian< Real >.

Definition at line 108 of file ROL_Reduced_AugmentedLagrangian_SimOpt.hpp.

References ROL::Reduced_AugmentedLagrangian_SimOpt< Real >::ngval_, and ROL::Reduced_AugmentedLagrangian_SimOpt< Real >::rAugLagSimOpt_.

template<class Real >

void ROL::Reduced_AugmentedLagrangian_SimOpt< 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.