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

#include <ROL_AugmentedLagrangian_SimOpt.hpp>

Inheritance diagram for ROL::AugmentedLagrangian_SimOpt< Real >:

Public Member Functions
	AugmentedLagrangian_SimOpt (const ROL::Ptr< Objective_SimOpt< Real > > &obj, const ROL::Ptr< Constraint_SimOpt< Real > > &con, const Vector< Real > &multiplier, const Real penaltyParameter, const Vector< Real > &simVec, const Vector< Real > &optVec, const Vector< Real > &conVec, ROL::ParameterList &parlist)

virtual void	update (const Vector< Real > &u, const Vector< Real > &z, bool flag=true, int iter=-1)
	Update objective function. u is an iterate, z is an iterate, flag = true if the iterate has changed, iter is the outer algorithm iterations count. More...

virtual Real	value (const Vector< Real > &u, const Vector< Real > &z, Real &tol)
	Compute value. More...

virtual void	gradient_1 (Vector< Real > &g, const Vector< Real > &u, const Vector< Real > &z, Real &tol)
	Compute gradient with respect to first component. More...

virtual void	gradient_2 (Vector< Real > &g, const Vector< Real > &u, const Vector< Real > &z, Real &tol)
	Compute gradient with respect to second component. More...

virtual void	hessVec_11 (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &u, const Vector< Real > &z, Real &tol)
	Apply Hessian approximation to vector. More...

virtual void	hessVec_12 (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &u, const Vector< Real > &z, Real &tol)

virtual void	hessVec_21 (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &u, const Vector< Real > &z, Real &tol)

virtual void	hessVec_22 (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &u, const Vector< Real > &z, Real &tol)

virtual Real	getObjectiveValue (const Vector< Real > &u, const Vector< Real > &z)

virtual void	getConstraintVec (Vector< Real > &c, const Vector< Real > &u, const Vector< Real > &z)

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

virtual void	update (const Vector< Real > &u, const Vector< Real > &z, UpdateType type, int iter=-1)

void	update (const Vector< Real > &x, UpdateType type, 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...

std::vector< std::vector< Real > >	checkGradient_1 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)

std::vector< std::vector< Real > >	checkGradient_1 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &g, const Vector< Real > &d, const bool printToStream, std::ostream &outStream, const int numSteps, const int order)

std::vector< std::vector< Real > >	checkGradient_1 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &g, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream, std::ostream &outStream, const int order)

std::vector< std::vector< Real > >	checkGradient_2 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)

std::vector< std::vector< Real > >	checkGradient_2 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &g, const Vector< Real > &d, const bool printToStream, std::ostream &outStream, const int numSteps, const int order)

std::vector< std::vector< Real > >	checkGradient_2 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &g, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream, std::ostream &outStream, const int order)

std::vector< std::vector< Real > >	checkHessVec_11 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)

std::vector< std::vector< Real > >	checkHessVec_11 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)

std::vector< std::vector< Real > >	checkHessVec_11 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &hv, const Vector< Real > &v, const bool printToStream, std::ostream &outStream, const int numSteps, const int order)

std::vector< std::vector< Real > >	checkHessVec_11 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &hv, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream, std::ostream &outStream, const int order)

std::vector< std::vector< Real > >	checkHessVec_12 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)

std::vector< std::vector< Real > >	checkHessVec_12 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)

std::vector< std::vector< Real > >	checkHessVec_12 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &hv, const Vector< Real > &v, const bool printToStream, std::ostream &outStream, const int numSteps, const int order)

std::vector< std::vector< Real > >	checkHessVec_12 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &hv, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream, std::ostream &outStream, const int order)

std::vector< std::vector< Real > >	checkHessVec_21 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)

std::vector< std::vector< Real > >	checkHessVec_21 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)

std::vector< std::vector< Real > >	checkHessVec_21 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &hv, const Vector< Real > &v, const bool printToStream, std::ostream &outStream, const int numSteps, const int order)

std::vector< std::vector< Real > >	checkHessVec_21 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &hv, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream, std::ostream &outStream, const int order)

std::vector< std::vector< Real > >	checkHessVec_22 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)

std::vector< std::vector< Real > >	checkHessVec_22 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)

std::vector< std::vector< Real > >	checkHessVec_22 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &hv, const Vector< Real > &v, const bool printToStream, std::ostream &outStream, const int numSteps, const int order)

std::vector< std::vector< Real > >	checkHessVec_22 (const Vector< Real > &u, const Vector< Real > &z, const Vector< Real > &hv, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream, std::ostream &outStream, const int order)

Public Member Functions inherited from ROL::Objective< Real >
virtual	~Objective ()

	Objective ()

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 Attributes
const ROL::Ptr < Objective_SimOpt< Real > >	obj_

ROL::Ptr < QuadraticPenalty_SimOpt < Real > >	pen_

Real	penaltyParameter_

ROL::Ptr< Vector< Real > >	dualSimVector_

ROL::Ptr< Vector< Real > >	dualOptVector_

Real	fval_

ROL::Ptr< Vector< Real > >	gradient1_

ROL::Ptr< Vector< Real > >	gradient2_

int	nfval_

int	ngval_

bool	scaleLagrangian_

bool	isValueComputed_

bool	isGradient1Computed_

bool	isGradient2Computed_

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_SimOpt< Real >

Provides the interface to evaluate the SimOpt augmented Lagrangian.

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

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

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

\[ \nabla^2_{uu} L_A(u,z,\lambda,\mu)v \approx \nabla^2_{uu} f(u,z) v + \mu c_u(u,z)^*\mathfrak{R} c_u(u,z)v, \quad \nabla^2_{uz} L_A(u,z,\lambda,\mu)v \approx \nabla^2_{uz} f(u,z) v + \mu c_u(u,z)^*\mathfrak{R} c_z(u,z)v, \]

\[ \nabla^2_{zu} L_A(u,z,\lambda,\mu)v \approx \nabla^2_{zu} f(u,z) v + \mu c_z(u,z)^*\mathfrak{R} c_u(u,z)v, \quad\text{and}\quad \nabla^2_{zz} L_A(u,z,\lambda,\mu)v \approx \nabla^2_{zz} f(u,z) v + \mu c_z(u,z)^*\mathfrak{R} c_z(u,z)v, \]

Definition at line 63 of file ROL_AugmentedLagrangian_SimOpt.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::AugmentedLagrangian_SimOpt< Real >::AugmentedLagrangian_SimOpt	(	const ROL::Ptr< Objective_SimOpt< Real > > &	obj,
		const ROL::Ptr< Constraint_SimOpt< Real > > &	con,
		const Vector< Real > &	multiplier,
		const Real	penaltyParameter,
		const Vector< Real > &	simVec,
		const Vector< Real > &	optVec,
		const Vector< Real > &	conVec,
		ROL::ParameterList &	parlist
	)

inline

Definition at line 92 of file ROL_AugmentedLagrangian_SimOpt.hpp.

References ROL::Vector< Real >::dual(), ROL::AugmentedLagrangian_SimOpt< Real >::dualOptVector_, ROL::AugmentedLagrangian_SimOpt< Real >::dualSimVector_, ROL::AugmentedLagrangian_SimOpt< Real >::gradient1_, ROL::AugmentedLagrangian_SimOpt< Real >::gradient2_, ROL::AugmentedLagrangian_SimOpt< Real >::pen_, and ROL::AugmentedLagrangian_SimOpt< Real >::scaleLagrangian_.

Member Function Documentation

template<class Real >

virtual void ROL::AugmentedLagrangian_SimOpt< Real >::update	(	const Vector< Real > &	u,
		const Vector< Real > &	z,
		bool	flag = `true`,
		int	iter = `-1`
	)

inlinevirtual

Update objective function. u is an iterate, z is an iterate, flag = true if the iterate has changed, iter is the outer algorithm iterations count.

Reimplemented from ROL::Objective_SimOpt< Real >.

Definition at line 116 of file ROL_AugmentedLagrangian_SimOpt.hpp.

References ROL::AugmentedLagrangian_SimOpt< Real >::isGradient1Computed_, ROL::AugmentedLagrangian_SimOpt< Real >::isGradient2Computed_, ROL::AugmentedLagrangian_SimOpt< Real >::isValueComputed_, ROL::AugmentedLagrangian_SimOpt< Real >::obj_, and ROL::AugmentedLagrangian_SimOpt< Real >::pen_.

template<class Real >

virtual Real ROL::AugmentedLagrangian_SimOpt< Real >::value	(	const Vector< Real > &	u,
		const Vector< Real > &	z,
		Real &	tol
	)

inlinevirtual

Compute value.

Implements ROL::Objective_SimOpt< Real >.

Definition at line 124 of file ROL_AugmentedLagrangian_SimOpt.hpp.

References ROL::AugmentedLagrangian_SimOpt< Real >::fval_, ROL::AugmentedLagrangian_SimOpt< Real >::isValueComputed_, ROL::AugmentedLagrangian_SimOpt< Real >::nfval_, ROL::AugmentedLagrangian_SimOpt< Real >::obj_, ROL::AugmentedLagrangian_SimOpt< Real >::pen_, ROL::AugmentedLagrangian_SimOpt< Real >::penaltyParameter_, and ROL::AugmentedLagrangian_SimOpt< Real >::scaleLagrangian_.

template<class Real >

virtual void ROL::AugmentedLagrangian_SimOpt< Real >::gradient_1	(	Vector< Real > &	g,
		const Vector< Real > &	u,
		const Vector< Real > &	z,
		Real &	tol
	)

inlinevirtual

Compute gradient with respect to first component.

Reimplemented from ROL::Objective_SimOpt< Real >.

Definition at line 140 of file ROL_AugmentedLagrangian_SimOpt.hpp.

template<class Real >

virtual void ROL::AugmentedLagrangian_SimOpt< Real >::gradient_2	(	Vector< Real > &	g,
		const Vector< Real > &	u,
		const Vector< Real > &	z,
		Real &	tol
	)

inlinevirtual

Compute gradient with respect to second component.

Reimplemented from ROL::Objective_SimOpt< Real >.

Definition at line 156 of file ROL_AugmentedLagrangian_SimOpt.hpp.

template<class Real >

virtual void ROL::AugmentedLagrangian_SimOpt< Real >::hessVec_11	(	Vector< Real > &	hv,
		const Vector< Real > &	v,
		const Vector< Real > &	u,
		const Vector< Real > &	z,
		Real &	tol
	)

inlinevirtual

Apply Hessian approximation to vector.

Reimplemented from ROL::Objective_SimOpt< Real >.

Definition at line 172 of file ROL_AugmentedLagrangian_SimOpt.hpp.

References ROL::AugmentedLagrangian_SimOpt< Real >::dualSimVector_, ROL::AugmentedLagrangian_SimOpt< Real >::obj_, ROL::AugmentedLagrangian_SimOpt< Real >::pen_, ROL::AugmentedLagrangian_SimOpt< Real >::penaltyParameter_, ROL::Vector< Real >::plus(), ROL::Vector< Real >::scale(), and ROL::AugmentedLagrangian_SimOpt< Real >::scaleLagrangian_.

template<class Real >

virtual void ROL::AugmentedLagrangian_SimOpt< Real >::hessVec_12	(	Vector< Real > &	hv,
		const Vector< Real > &	v,
		const Vector< Real > &	u,
		const Vector< Real > &	z,
		Real &	tol
	)

inlinevirtual

Reimplemented from ROL::Objective_SimOpt< Real >.

Definition at line 185 of file ROL_AugmentedLagrangian_SimOpt.hpp.

References ROL::AugmentedLagrangian_SimOpt< Real >::dualSimVector_, ROL::AugmentedLagrangian_SimOpt< Real >::obj_, ROL::AugmentedLagrangian_SimOpt< Real >::pen_, ROL::AugmentedLagrangian_SimOpt< Real >::penaltyParameter_, ROL::Vector< Real >::plus(), ROL::Vector< Real >::scale(), and ROL::AugmentedLagrangian_SimOpt< Real >::scaleLagrangian_.

template<class Real >

virtual void ROL::AugmentedLagrangian_SimOpt< Real >::hessVec_21	(	Vector< Real > &	hv,
		const Vector< Real > &	v,
		const Vector< Real > &	u,
		const Vector< Real > &	z,
		Real &	tol
	)

inlinevirtual

Reimplemented from ROL::Objective_SimOpt< Real >.

Definition at line 198 of file ROL_AugmentedLagrangian_SimOpt.hpp.

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

template<class Real >

virtual void ROL::AugmentedLagrangian_SimOpt< Real >::hessVec_22	(	Vector< Real > &	hv,
		const Vector< Real > &	v,
		const Vector< Real > &	u,
		const Vector< Real > &	z,
		Real &	tol
	)