MOOCHO (Single Doxygen Collection) Version of the Day
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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:
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List of all members.

Private Attributes

quasi_newton_stats_iq_member quasi_newton_stats_

Initializers/constructors

enum  EInitializationMethod { SCALE_IDENTITY, SCALE_DIAGONAL, SCALE_DIAGONAL_ABS }
  More...
 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.
 STANDARD_MEMBER_COMPOSITION_MEMBERS (value_type, max_cond)
 Maximum condition (l2 norm) for the intial matrix = (max(diag(i))/min(diag(i)).
 STANDARD_MEMBER_COMPOSITION_MEMBERS (value_type, min_diag)
 The absolute minimum value of a diagonal element.
 STANDARD_MEMBER_COMPOSITION_MEMBERS (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
 

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.


Member Enumeration Documentation

Enumerator:
SCALE_IDENTITY 
SCALE_DIAGONAL 
SCALE_DIAGONAL_ABS 

Definition at line 78 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 
)

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 
) [virtual]
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 [virtual]

Reimplemented from IterationPack::AlgorithmStep.

Definition at line 278 of file MoochoPack_InitFinDiffReducedHessian_Step.cpp.


Member Data Documentation


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