MoochoPack::InitFinDiffReducedHessian_Step Class Reference

Initializes the reduced hessian using a single finite difference along the null space of the constraints. More...

#include <MoochoPack_InitFinDiffReducedHessian_Step.hpp>

Inheritance diagram for MoochoPack::InitFinDiffReducedHessian_Step:

Initializers/constructors
enum	EInitializationMethod
	InitFinDiffReducedHessian_Step (EInitializationMethod initialization_method=SCALE_IDENTITY, value_type max_cond=1e+1, value_type min_diag=1e-8, value_type step_scale=1e-1)
	STANDARD_MEMBER_COMPOSITION_MEMBERS (EInitializationMethod, initialization_method)
	The initialization method for setting the diagonal. More...
	STANDARD_MEMBER_COMPOSITION_MEMBERS (value_type, max_cond)
	Maximum condition (l2 norm) for the intial matrix = (max(diag(i))/min(diag(i)). More...
	STANDARD_MEMBER_COMPOSITION_MEMBERS (value_type, min_diag)
	The absolute minimum value of a diagonal element. More...
	STANDARD_MEMBER_COMPOSITION_MEMBERS (value_type, step_scale)
	The scaling of the step length u = step_scale / ||Z*e||inf. More...

Overridden from AlgorithmStep
bool	do_step (Algorithm &algo, poss_type step_poss, IterationPack::EDoStepType type, poss_type assoc_step_poss)
void	print_step (const Algorithm &algo, poss_type step_poss, IterationPack::EDoStepType type, poss_type assoc_step_poss, std::ostream &out, const std::string &leading_str) const

Detailed Description

Initializes the reduced hessian using a single finite difference along the null space of the constraints.

A single finite difference correction is computed along:\

x_fd = x_k + u * Z * e

The step length is set to u = step_scale / ||Z*e||inf. The step length is cut back if the point x_fd is outside the relaxed variable bounds.

The finite difference is then computed as:

rGf_fd = ( Z_k' * g(x_k + u * Z*e) - rGf_k ) / u

The diagonal terms of the reduced hessian are then set as:

diag(i) = max( ||rGf_fd||inf , smallest_ele ) if initialization_method == SCALE_IDENTITY\ diag(i) = max( rGf_fd(i) , smallest_ele ) if initialization_method == SCALE_DIAGONAL\ diag(i) = max( abs(rGf_fd(i)), smallest_ele ) if initialization_method == SCALE_DIAGONAL_ABS\

Where:

smallest_ele = max( ||rGf_fd||inf / max_cond , min_diag )

Since the matrix is diagonal the diagonal is equal to the eigenvalues of the matrix. Therefore you can show that the condition number measured in any norm is max(diag(i))/min(diag(i)). therefore we just need to limit the smallest diagonal as diag(i) > max(diag(i)) / max_cond.

Definition at line 82 of file MoochoPack_InitFinDiffReducedHessian_Step.hpp.

Member Enumeration Documentation

enum MoochoPack::InitFinDiffReducedHessian_Step::EInitializationMethod

Definition at line 91 of file MoochoPack_InitFinDiffReducedHessian_Step.hpp.

Constructor & Destructor Documentation

MoochoPack::InitFinDiffReducedHessian_Step::InitFinDiffReducedHessian_Step	(	EInitializationMethod	initialization_method = SCALE_IDENTITY,
		value_type	max_cond = 1e+1,
		value_type	min_diag = 1e-8,
		value_type	step_scale = 1e-1
	)

Definition at line 69 of file MoochoPack_InitFinDiffReducedHessian_Step.cpp.

Member Function Documentation

MoochoPack::InitFinDiffReducedHessian_Step::STANDARD_MEMBER_COMPOSITION_MEMBERS	(	EInitializationMethod	,
		initialization_method
	)

The initialization method for setting the diagonal.

MoochoPack::InitFinDiffReducedHessian_Step::STANDARD_MEMBER_COMPOSITION_MEMBERS	(	value_type	,
		max_cond
	)

Maximum condition (l2 norm) for the intial matrix = (max(diag(i))/min(diag(i)).

MoochoPack::InitFinDiffReducedHessian_Step::STANDARD_MEMBER_COMPOSITION_MEMBERS	(	value_type	,
		min_diag
	)

The absolute minimum value of a diagonal element.

MoochoPack::InitFinDiffReducedHessian_Step::STANDARD_MEMBER_COMPOSITION_MEMBERS	(	value_type	,
		step_scale
	)

The scaling of the step length u = step_scale / ||Z*e||inf.

bool MoochoPack::InitFinDiffReducedHessian_Step::do_step	(	Algorithm &	algo,
		poss_type	step_poss,
		IterationPack::EDoStepType	type,
		poss_type	assoc_step_poss
	)

Definition at line 81 of file MoochoPack_InitFinDiffReducedHessian_Step.cpp.

void MoochoPack::InitFinDiffReducedHessian_Step::print_step	(	const Algorithm &	algo,
		poss_type	step_poss,
		IterationPack::EDoStepType	type,
		poss_type	assoc_step_poss,
		std::ostream &	out,
		const std::string &	leading_str
	)		const

Definition at line 291 of file MoochoPack_InitFinDiffReducedHessian_Step.cpp.

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

• MoochoPack_InitFinDiffReducedHessian_Step.hpp
• MoochoPack_InitFinDiffReducedHessian_Step.cpp