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:

[legend]List of all members.

Initializers/constructors
enum	EInitializationMethod
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	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)
void	initialization_method (const EInitializationMethod &initialization_method)
	The initialization method for setting the diagonal.
void	max_cond (const value_type &max_cond)
	Maximum condition (l2 norm) for the intial matrix = (max(diag(i))/min(diag(i)).
void	min_diag (const value_type &min_diag)
	The absolute minimum value of a diagonal element.
void	step_scale (const value_type &step_scale)
	The scaling of the step length u = step_scale / ||Z*e||inf.
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

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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 69 of file MoochoPack_InitFinDiffReducedHessian_Step.hpp.

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Member Enumeration Documentation

enum MoochoPack::InitFinDiffReducedHessian_Step::EInitializationMethod

Definition at line 78 of file MoochoPack_InitFinDiffReducedHessian_Step.hpp.

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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 56 of file MoochoPack_InitFinDiffReducedHessian_Step.cpp.

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Member Function Documentation

void MoochoPack::InitFinDiffReducedHessian_Step::initialization_method (  const EInitializationMethod &  initialization_method  )  [inline]

The initialization method for setting the diagonal. Definition at line 89 of file MoochoPack_InitFinDiffReducedHessian_Step.hpp.

void MoochoPack::InitFinDiffReducedHessian_Step::max_cond (  const value_type &  max_cond  )  [inline]

Maximum condition (l2 norm) for the intial matrix = (max(diag(i))/min(diag(i)). Definition at line 92 of file MoochoPack_InitFinDiffReducedHessian_Step.hpp.

void MoochoPack::InitFinDiffReducedHessian_Step::min_diag (  const value_type &  min_diag  )  [inline]

The absolute minimum value of a diagonal element. Definition at line 95 of file MoochoPack_InitFinDiffReducedHessian_Step.hpp.

void MoochoPack::InitFinDiffReducedHessian_Step::step_scale (  const value_type &  step_scale  )  [inline]

The scaling of the step length u = step_scale / ||Z*e||inf. Definition at line 98 of file MoochoPack_InitFinDiffReducedHessian_Step.hpp.

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

Definition at line 68 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 278 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

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