Provides the interface to evaluate nonlinear least squares objective functions. More...

#include <ROL_NonlinearLeastSquaresObjective.hpp>

Inheritance diagram for ROL::NonlinearLeastSquaresObjective< Real >:

Public Member Functions
	NonlinearLeastSquaresObjective (const Ptr< Constraint< Real > > &con, const Vector< Real > &optvec, const Vector< Real > &convec, const bool GNH=false)
	Constructor. More...

void	update (const Vector< Real > &x, UpdateType type, int iter=-1) override
	Update objective function. More...

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

Real	value (const Vector< Real > &x, Real &tol) override
	Compute value. More...

void	gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol) override
	Compute gradient. More...

void	hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) override
	Apply Hessian approximation to vector. More...

void	precond (Vector< Real > &Pv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) override
	Apply preconditioner to vector. More...

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

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	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...

Private Attributes
const Ptr< Constraint< Real > >	con_

const bool	GaussNewtonHessian_

Ptr< Vector< Real > >	c1_

Ptr< Vector< Real > >	c2_

Ptr< Vector< Real > >	c1dual_

Ptr< Vector< Real > >	x_

Additional Inherited Members
Protected Member Functions inherited from ROL::Objective< Real >
const std::vector< Real >	getParameter (void) const

Detailed Description

template<typename Real>
class ROL::NonlinearLeastSquaresObjective< Real >

Provides the interface to evaluate nonlinear least squares objective functions.

ROL's nonlinear least squares objective function interface constructs the the nonlinear least squares objective function associated with the equality constraint \(c(x)=0\). That is,

\[ J(x) = \langle \mathfrak{R} c(x),c(x) \rangle_{\mathcal{C}^*,\mathcal{C}} \]

where \(c:\mathcal{X}\to\mathcal{C}\) and \(\mathfrak{R}\in\mathcal{L}( \mathcal{C},\mathcal{C}^*)\) denotes the Riesz map from \(\mathcal{C}\) into \(\mathcal{C}^*\).

Definition at line 39 of file ROL_NonlinearLeastSquaresObjective.hpp.

Constructor & Destructor Documentation

template<typename Real>

ROL::NonlinearLeastSquaresObjective< Real >::NonlinearLeastSquaresObjective	(	const Ptr< Constraint< Real > > &	con,
		const Vector< Real > &	optvec,
		const Vector< Real > &	convec,
		const bool	GNH = `false`
	)

Constructor.

This function constructs a nonlinear least squares objective function.

Parameters

[in]	con	is the nonlinear equation to be solved.
[in]	vec	is a constraint space vector used for cloning.
[in]	GHN	is a flag dictating whether or not to use the Gauss-Newton Hessian.

Definition at line 16 of file ROL_NonlinearLeastSquaresObjective_Def.hpp.

References ROL::NonlinearLeastSquaresObjective< Real >::c1_, ROL::NonlinearLeastSquaresObjective< Real >::c1dual_, ROL::NonlinearLeastSquaresObjective< Real >::c2_, ROL::Vector< Real >::clone(), ROL::Vector< Real >::dual(), and ROL::NonlinearLeastSquaresObjective< Real >::x_.

Member Function Documentation

template<typename Real >

void ROL::NonlinearLeastSquaresObjective< Real >::update	(	const Vector< Real > &	x,
		UpdateType	type,
		int	iter = `-1`
	)

overridevirtual

Update objective function.

This function updates the objective function at new iterations.

Parameters

[in]	x	is the new iterate.
[in]	type	is the type of update requested.
[in]	iter	is the outer algorithm iterations count.

Reimplemented from ROL::Objective< Real >.

Definition at line 27 of file ROL_NonlinearLeastSquaresObjective_Def.hpp.

template<typename Real >

void ROL::NonlinearLeastSquaresObjective< Real >::update	(	const Vector< Real > &	x,
		bool	flag = `true`,
		int	iter = `-1`
	)

overridevirtual

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 35 of file ROL_NonlinearLeastSquaresObjective_Def.hpp.

template<typename Real >

Real ROL::NonlinearLeastSquaresObjective< Real >::value	(	const Vector< Real > &	x,
		Real &	tol
	)

overridevirtual

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 43 of file ROL_NonlinearLeastSquaresObjective_Def.hpp.

template<typename Real >

void ROL::NonlinearLeastSquaresObjective< Real >::gradient	(	Vector< Real > &	g,
		const Vector< Real > &	x,
		Real &	tol
	)

overridevirtual

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 49 of file ROL_NonlinearLeastSquaresObjective_Def.hpp.

template<typename Real >

void ROL::NonlinearLeastSquaresObjective< Real >::hessVec	(	Vector< Real > &	hv,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol
	)

overridevirtual

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.

Reimplemented from ROL::Objective< Real >.

Definition at line 54 of file ROL_NonlinearLeastSquaresObjective_Def.hpp.

References ROL::Vector< Real >::dual(), and ROL::Vector< Real >::plus().

template<typename Real >

void ROL::NonlinearLeastSquaresObjective< Real >::precond	(	Vector< Real > &	Pv,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol
	)

overridevirtual

Apply preconditioner to vector.

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

Parameters

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