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 ROL::Ptr< Constraint< Real > > &con, const Vector< Real > &optvec, const Vector< Real > &convec, const bool GNH=false)
	Constructor. More...

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...

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

Public Member Functions inherited from ROL::Objective< Real >
virtual	~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 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
const ROL::Ptr< Constraint < Real > >	con_

const bool	GaussNewtonHessian_

ROL::Ptr< Vector< Real > >	c1_

ROL::Ptr< Vector< Real > >	c2_

ROL::Ptr< Vector< Real > >	c1dual_

ROL::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<class 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 73 of file ROL_NonlinearLeastSquaresObjective.hpp.

Constructor & Destructor Documentation

template<class Real>

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

inline

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 88 of file ROL_NonlinearLeastSquaresObjective.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<class Real>

void ROL::NonlinearLeastSquaresObjective< 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::Objective< Real >.

Definition at line 98 of file ROL_NonlinearLeastSquaresObjective.hpp.

References ROL::NonlinearLeastSquaresObjective< Real >::c1_, ROL::NonlinearLeastSquaresObjective< Real >::c1dual_, and ROL::NonlinearLeastSquaresObjective< Real >::con_.

template<class Real>

Real ROL::NonlinearLeastSquaresObjective< 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.

Implements ROL::Objective< Real >.

Definition at line 105 of file ROL_NonlinearLeastSquaresObjective.hpp.

References ROL::NonlinearLeastSquaresObjective< Real >::c1_, and ROL::NonlinearLeastSquaresObjective< Real >::c1dual_.

template<class Real>

void ROL::NonlinearLeastSquaresObjective< 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::Objective< Real >.

Definition at line 110 of file ROL_NonlinearLeastSquaresObjective.hpp.

References ROL::NonlinearLeastSquaresObjective< Real >::c1dual_, and ROL::NonlinearLeastSquaresObjective< Real >::con_.

template<class Real>

void ROL::NonlinearLeastSquaresObjective< 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.