Base class to support a user defined merit function that can be passed to line searches and directions through the parameter list. More...

#include <NOX_MeritFunction_Generic.H>

Inheritance diagram for NOX::MeritFunction::Generic:

[legend]

Public Member Functions
	Generic ()
	Default Constructor.

virtual	~Generic ()
	Destructor.

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

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.

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.

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

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.

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

Detailed Description

Base class to support a user defined merit function that can be passed to line searches and directions through the parameter list.

This class allows the user to define their own merit function for use in a line search. Each line search type will specify in it's input parameter list if it supports this functionality.

To create and use a user defined merit function:

Create a merit function that derives from NOX::Parameter::MeritFunction. For example, the merit function Foo might be defined as shown below.

class Foo : public NOX::Parameter::MeritFunction {

// Insert class definition here

}
Create the appropriate entries in the parameter list, as follows.

Foo foo();

params.sublist("Solver Options").set("User Defined Merit Function", foo);

Member Function Documentation

◆ computef()

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

pure virtual

Computes the merit function, .

Implemented in NOX::Thyra::WeightedMeritFunction, and NOX::MeritFunction::SumOfSquares.

◆ computeGradient()

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

pure virtual

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

Implemented in NOX::Thyra::WeightedMeritFunction, and NOX::MeritFunction::SumOfSquares.

◆ computeQuadraticMinimizer()

virtual void NOX::MeritFunction::Generic::computeQuadraticMinimizer	(	const NOX::Abstract::Group &	grp,
		NOX::Abstract::Vector &	result
	)		const

pure 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:

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

Implemented in NOX::Thyra::WeightedMeritFunction, and NOX::MeritFunction::SumOfSquares.

◆ computeQuadraticModel()

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

pure 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).

Implemented in NOX::Thyra::WeightedMeritFunction, and NOX::MeritFunction::SumOfSquares.

◆ computeSlope()

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

pure 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 $\zeta$ :