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)
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)
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.
	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.
	AugmentedLagrangian ()
	Null constructor.
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::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.

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::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

◆ Reduced_AugmentedLagrangian_SimOpt()

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 )