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.
virtual Real	value (const Vector< Real > &u, const Vector< Real > &z, Real &tol)
	Compute value.
virtual void	gradient_1 (Vector< Real > &g, const Vector< Real > &u, const Vector< Real > &z, Real &tol)
	Compute gradient with respect to first component.
virtual void	gradient_2 (Vector< Real > &g, const Vector< Real > &u, const Vector< Real > &z, Real &tol)
	Compute gradient with respect to second component.
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.
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)
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)
Real	value (const Vector< Real > &x, Real &tol)
void	gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol)
void	hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
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::ROL::Objective< Real >
virtual	~Objective ()
	Objective ()
virtual void	update (const Vector< Real > &x, UpdateType type, int iter=-1)
	Update objective function.
virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update objective function.
virtual Real	value (const Vector< Real > &x, Real &tol)=0
	Compute value.
virtual void	gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol)
	Compute gradient.
virtual Real	dirDeriv (const Vector< Real > &x, const Vector< Real > &d, Real &tol)
	Compute directional derivative.
virtual void	hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply Hessian approximation to vector.
virtual void	invHessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply inverse Hessian approximation to vector.
virtual void	precond (Vector< Real > &Pv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply preconditioner to vector.
virtual void	prox (Vector< Real > &Pv, const Vector< Real > &v, Real t, Real &tol)
	Compute the proximity operator.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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::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

◆ AugmentedLagrangian_SimOpt()

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(), dualOptVector_, dualSimVector_, fval_, gradient1_, gradient2_, isGradient1Computed_, isGradient2Computed_, isValueComputed_, nfval_, ngval_, obj_, pen_, penaltyParameter_, and scaleLagrangian_.

Member Function Documentation

◆ update()

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 isGradient1Computed_, isGradient2Computed_, isValueComputed_, obj_, and pen_.

◆ value()

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 fval_, isValueComputed_, nfval_, obj_, pen_, penaltyParameter_, and scaleLagrangian_.

◆ gradient_1()

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.

References dualSimVector_, gradient1_, isGradient1Computed_, ngval_, obj_, pen_, penaltyParameter_, ROL::Vector< Real >::plus(), ROL::Vector< Real >::scale(), scaleLagrangian_, and ROL::Vector< Real >::set().

◆ gradient_2()

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.

References dualOptVector_, gradient2_, isGradient2Computed_, ngval_, obj_, pen_, penaltyParameter_, ROL::Vector< Real >::plus(), ROL::Vector< Real >::scale(), scaleLagrangian_, and ROL::Vector< Real >::set().

◆ hessVec_11()

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

◆ hessVec_12()

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

◆ hessVec_21()

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

◆ hessVec_22()

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 )