Implementation of merit function for implicitly weighted norm. More...

#include <NOX_MeritFunction_Weighted.hpp>

Inheritance diagram for NOX::Thyra::WeightedMeritFunction:

Collaboration diagram for NOX::Thyra::WeightedMeritFunction:

Public Member Functions
	WeightedMeritFunction (const Teuchos::RCP< const ::Thyra::VectorBase< double > > weights, bool optimizeSlopeCalc=true)
	Constructor.

	WeightedMeritFunction (const WeightedMeritFunction &source)
	Copy constructor.

	~WeightedMeritFunction ()
	Destructor.

virtual const std::string &	name () const
	Returns the name of the merit function.

virtual std::ostream &	print (std::ostream &os, int indent=0) const

virtual double	computef (const NOX::Abstract::Group &group) const
	Computes the merit function, .

virtual void	computeGradient (const NOX::Abstract::Group &group, NOX::Abstract::Vector &result) const
	Computes the gradient of the merit function, $\nabla f$ , and returns the result in the `result` vector.

virtual double	computeSlope (const NOX::Abstract::Vector &dir, const NOX::Abstract::Group &group) const
	Computes the inner product of the given direction and the gradient associated with the merit function. Returns the steepest descent direction in the `result` vector.

virtual double	computeQuadraticModel (const NOX::Abstract::Vector &dir, const NOX::Abstract::Group &group) const
	Compute the quadratic model, , for the given merit function.

virtual void	computeQuadraticMinimizer (const NOX::Abstract::Group &grp, NOX::Abstract::Vector &result) const
	Computes the vector in the steepest descent direction that minimizes the quadratic model.

virtual bool	computeSteepestDescentDir (const NOX::Abstract::Group &group, NOX::Abstract::Vector &result) const

Public Member Functions inherited from NOX::MeritFunction::Generic
	Generic ()
	Default Constructor.

virtual	~Generic ()
	Destructor.

Detailed Description

Implementation of merit function for implicitly weighted norm.

NOTE: The nox vectors in this object are always unweighted (we always apply the weights explicitly)! Be careful about using norms and innerProducts from incoming nox objects as these will have the implicit weighting attached.

Member Function Documentation

◆ computef()

double NOX::Thyra::WeightedMeritFunction::computef ( const NOX::Abstract::Group & grp ) const

virtual

Computes the merit function, .

Implements NOX::MeritFunction::Generic.

References NOX::Abstract::Group::getFPtr(), and NOX::Abstract::Group::isF().

◆ computeGradient()

void NOX::Thyra::WeightedMeritFunction::computeGradient	(	const NOX::Abstract::Group &	group,
		NOX::Abstract::Vector &	result
	)		const

virtual

Computes the gradient of the merit function, $\nabla f$ , and returns the result in the result vector.

Implements NOX::MeritFunction::Generic.

References NOX::Abstract::Group::applyJacobianTranspose(), NOX::Abstract::Group::getF(), NOX::Thyra::Vector::getThyraVector(), NOX::Abstract::Group::isF(), NOX::Abstract::Group::isJacobian(), and NOX::Abstract::Group::Ok.

◆ computeQuadraticMinimizer()

void NOX::Thyra::WeightedMeritFunction::computeQuadraticMinimizer	(	const NOX::Abstract::Group &	grp,
		NOX::Abstract::Vector &	result
	)		const

virtual

Computes the vector in the steepest descent direction that minimizes the quadratic model.

The quadratic model is defined as:

$m(d) = f(x) + \nabla f(x)^T d + d^T \nabla^2 f(x) d + d^T \mathbf{B} d$

where is ideally the Hessian of the merit function, $\nabla^2 f(x)$ , but can be approximated with the restriction that it is a symmetric and has uniform boundedness in the iterate sequence (see J. Nocedal and S. J. Wright, "Numerical Optimization", Springer, 1999. Chapters 4 and 6).

The result vector should be computed as:

$result = -\frac{\nabla f^T \nabla f}{\nabla f^T B \nabla f} \nabla f$

Implements NOX::MeritFunction::Generic.

◆ computeQuadraticModel()

double NOX::Thyra::WeightedMeritFunction::computeQuadraticModel	(	const NOX::Abstract::Vector &	dir,
		const NOX::Abstract::Group &	grp
	)		const

virtual

Compute the quadratic model, , for the given merit function.

Computes and returns :

$m(d) = f(x) + \nabla f(x)^T d + d^T \nabla^2 f(x) d + d^T \mathbf{B} d$

Here represents the input parameter dir. is the Hessian of the merit function, $\nabla^2 f(x)$ , but can be approximated with the restriction that it is a symmetric and has uniform boundedness in the iterate sequence (see J. Nocedal and S. J. Wright, "Numerical Optimization", Springer, 1999. Chapters 4 and 6).

Implements NOX::MeritFunction::Generic.

References NOX::Abstract::Group::applyJacobian().

◆ computeSlope()

double NOX::Thyra::WeightedMeritFunction::computeSlope	(	const NOX::Abstract::Vector &	dir,
		const NOX::Abstract::Group &	grp
	)		const

virtual

Computes the inner product of the given direction and the gradient associated with the merit function. Returns the steepest descent direction in the result vector.

Calculates and returns $\zeta$ :