Sum of squares merit function. More...

#include <NOX_MeritFunction_SumOfSquares.H>

Inheritance diagram for NOX::MeritFunction::SumOfSquares:

Collaboration diagram for NOX::MeritFunction::SumOfSquares:

Public Member Functions
	SumOfSquares (const Teuchos::RCP< NOX::Utils > &u)
	Constructor.

virtual	~SumOfSquares ()
	Destructor.

virtual double	computef (const NOX::Abstract::Group &grp) const
	Computes the merit function, $f(x) = \frac{1}{2}\\| F(x) \\|^2$ . More...

virtual void	computeGradient (const NOX::Abstract::Group &group, NOX::Abstract::Vector &result) const
	Computes the gradient, $g = \nabla f(x) = J(x)^T F(x)$ . More...

virtual double	computeSlope (const NOX::Abstract::Vector &dir, const NOX::Abstract::Group &grp) const
	Computes the slope, $s(x,d) = d^T \nabla f(x) = d^T J(x)^T F(x)$ . More...

virtual double	computeQuadraticModel (const NOX::Abstract::Vector &dir, const NOX::Abstract::Group &grp) const
	Computes the quadratic model, $m(x,d) = f(x) + \nabla f(x)^T d + d^T \nabla^2 f(x) d$ . More...

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. More...

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

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

virtual	~Generic ()
	Destructor.

virtual double	computef (const NOX::Abstract::Group &grp) const =0
	Computes the merit function, . More...

virtual void	computeGradient (const NOX::Abstract::Group &group, NOX::Abstract::Vector &result) const =0
	Computes the gradient of the merit function, $\nabla f$ , and returns the result in the `result` vector. More...

virtual double	computeSlope (const NOX::Abstract::Vector &dir, const NOX::Abstract::Group &grp) const =0
	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. More...

virtual double	computeQuadraticModel (const NOX::Abstract::Vector &dir, const NOX::Abstract::Group &grp) const =0
	Compute the quadratic model, , for the given merit function. More...

virtual void	computeQuadraticMinimizer (const NOX::Abstract::Group &grp, NOX::Abstract::Vector &result) const =0
	Computes the vector in the steepest descent direction that minimizes the quadratic model. More...

virtual const std::string &	name () const =0
	Returns the name of the merit function. More...

Detailed Description

Sum of squares merit function.

A basic merit function used in many nonlinear equation solvers:

$f = \frac{1}{2} \| F(x) \| ^2$

Where the norm is the 2-Norm using the NOX::Abstract::Vector's inner product.

This is the default merit function used in nox.

This merit function is taken from: J. E. Dennis Jr. and Robert B. Schnabel, "Numerical Methods for Unconstrained Optimization and Nonlinear Equations," Prentice Hall, 1983

Member Function Documentation

◆ computef()

double NOX::MeritFunction::SumOfSquares::computef ( const NOX::Abstract::Group & grp ) const

virtual

Computes the merit function, $f(x) = \frac{1}{2}\| F(x) \|^2$ .

Implements NOX::MeritFunction::Generic.

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

◆ computeGradient()

void NOX::MeritFunction::SumOfSquares::computeGradient	(	const NOX::Abstract::Group &	group,
		NOX::Abstract::Vector &	result
	)		const

virtual

Computes the gradient, $g = \nabla f(x) = J(x)^T F(x)$ .

Implements NOX::MeritFunction::Generic.

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

◆ computeQuadraticMinimizer()

void NOX::MeritFunction::SumOfSquares::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.

Computes the vector result:

$result = \frac{\nabla f^T \nabla f}{\nabla f^T B \nabla f} \nabla f = -\frac{(J^T F)^T (J^T F)}{(J J^T F)^T (J J^T F)} J^T F$

Implements NOX::MeritFunction::Generic.

References NOX::Abstract::Group::applyJacobian(), NOX::Abstract::Vector::clone(), NOX::Abstract::Group::getF(), NOX::Abstract::Vector::innerProduct(), NOX::Abstract::Group::isF(), NOX::Abstract::Group::isJacobian(), NOX::Abstract::Group::Ok, NOX::Abstract::Vector::scale(), and NOX::ShapeCopy.

◆ computeQuadraticModel()

double NOX::MeritFunction::SumOfSquares::computeQuadraticModel	(	const NOX::Abstract::Vector &	dir,
		const NOX::Abstract::Group &	grp
	)		const

virtual

Computes the quadratic model, $m(x,d) = f(x) + \nabla f(x)^T d + d^T \nabla^2 f(x) d$ .

We approximate $\nabla^2f(x) \approx J^TJ$ :

$m(d) = f(x) + (J(x)^T F)^T d + \frac{1}{2} d^T B d$

Implements NOX::MeritFunction::Generic.

References NOX::Abstract::Group::applyJacobian(), NOX::Abstract::Vector::clone(), and NOX::Abstract::Group::getF().

◆ computeSlope()

double NOX::MeritFunction::SumOfSquares::computeSlope	(	const NOX::Abstract::Vector &	dir,
		const NOX::Abstract::Group &	grp
	)		const

virtual

Computes the slope, $s(x,d) = d^T \nabla f(x) = d^T J(x)^T F(x)$ .

If the Jacobian is not computed in the grp object, then the slope can be approximated using directional derivatives. More information can be found in the method computeSlopeWithoutJac.

Implements NOX::MeritFunction::Generic.

References NOX::Abstract::Vector::clone(), NOX::Abstract::Group::getF(), NOX::Abstract::Vector::innerProduct(), NOX::Abstract::Group::isGradient(), and NOX::Abstract::Group::isJacobian().

◆ name()

const std::string & NOX::MeritFunction::SumOfSquares::name ( ) const

virtual

Returns the name of the merit function.

Implements NOX::MeritFunction::Generic.

The documentation for this class was generated from the following files:

NOX_MeritFunction_SumOfSquares.H
NOX_MeritFunction_SumOfSquares.C

Public Member Functions

Detailed Description

Member Function Documentation

◆ computef()

◆ computeGradient()

◆ computeQuadraticMinimizer()

◆ computeQuadraticModel()

◆ computeSlope()

◆ name()