Reference documentation for deal.II version Git b33e53217d 2019-05-21 07:35:10 -0400
\(\newcommand{\dealcoloneq}{\mathrel{\vcenter{:}}=}\)
Classes | Public Types | Public Member Functions | Protected Attributes | List of all members
SolverBFGS< VectorType > Class Template Reference

#include <deal.II/optimization/solver_bfgs.h>

Inheritance diagram for SolverBFGS< VectorType >:
[legend]

Classes

struct  AdditionalData
 

Public Types

typedef VectorType::value_type Number
 
- Public Types inherited from SolverBase< VectorType >
using vector_type = VectorType
 

Public Member Functions

 SolverBFGS (SolverControl &residual_control, const AdditionalData &data=AdditionalData())
 
void solve (const std::function< Number(const VectorType &x, VectorType &g)> &compute, VectorType &x)
 
boost::signals2::connection connect_line_search_slot (const std::function< Number(Number &f, VectorType &x, VectorType &g, const VectorType &p)> &slot)
 
boost::signals2::connection connect_preconditioner_slot (const std::function< void(VectorType &g, const FiniteSizeHistory< VectorType > &s, const FiniteSizeHistory< VectorType > &y)> &slot)
 
- Public Member Functions inherited from SolverBase< VectorType >
 SolverBase (SolverControl &solver_control, VectorMemory< VectorType > &vector_memory)
 
 SolverBase (SolverControl &solver_control)
 
boost::signals2::connection connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate)> &slot)
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&) noexcept
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&) noexcept
 
void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
 
unsigned int n_subscriptions () const
 
template<typename StreamType >
void list_subscribers (StreamType &stream) const
 
void list_subscribers () const
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Protected Attributes

const AdditionalData additional_data
 
boost::signals2::signal< Number(Number &f, VectorType &x, VectorType &g, const VectorType &p)> line_search_signal
 
boost::signals2::signal< void(VectorType &g, const FiniteSizeHistory< VectorType > &s, const FiniteSizeHistory< VectorType > &y)> preconditioner_signal
 
- Protected Attributes inherited from SolverBase< VectorType >
GrowingVectorMemory< VectorType > static_vector_memory
 
VectorMemory< VectorType > & memory
 
boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate), StateCombineriteration_status
 

Additional Inherited Members

- Static Public Member Functions inherited from Subscriptor
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
 

Detailed Description

template<typename VectorType>
class SolverBFGS< VectorType >

Implement the limited memory BFGS minimization method.

This class implements a method to minimize a given function for which only the values of the function and its derivatives, but not its second derivatives are available. The BFGS method is a variation of the Newton method for function minimization in which the Hessian matrix is only approximated. In particular, the Hessian is updated using the formula of Broyden, Fletcher, Goldfarb, and Shanno (BFGS):

\begin{align*} H^{(k+1)} &= \left[ I-\rho_{(k)} s^{(k)} \otimes y^{(k)} \right] H^{(k)} \left[ I -\rho^{(k)} y^{(k)} \otimes s^{(k)} \right] + \rho^{(k)} s^{(k)} \otimes s^{(k)} \\ y^{(k)} &\dealcoloneq g^{(k+1)} - g^{(k)} \\ s^{(k)} &\dealcoloneq x^{(k+1)} - x^{(k)} \\ \rho^{(k)} &\dealcoloneq \frac{1}{y^{(k)} \cdot s^{(k)}} \end{align*}

for a symmetric positive definite \(H\). Limited memory variant is implemented via the two-loop recursion.

Author
Denis Davydov, 2018

Definition at line 56 of file solver_bfgs.h.

Member Typedef Documentation

◆ Number

template<typename VectorType >
typedef VectorType::value_type SolverBFGS< VectorType >::Number

Number type.

Definition at line 62 of file solver_bfgs.h.

Constructor & Destructor Documentation

◆ SolverBFGS()

template<typename VectorType >
SolverBFGS< VectorType >::SolverBFGS ( SolverControl residual_control,
const AdditionalData data = AdditionalData() 
)
explicit

Constructor.

Member Function Documentation

◆ solve()

template<typename VectorType >
void SolverBFGS< VectorType >::solve ( const std::function< Number(const VectorType &x, VectorType &g)> &  compute,
VectorType &  x 
)

Solve the unconstrained minimization problem

\[ \min_{\mathbf x} f(\mathbf x) \]

starting from initial state x.

The function compute takes two arguments indicating the values of \(x\) and of the gradient \(g=\nabla f(\mathbf x)=\frac{\partial f}{\partial \mathbf x}\). When called, it needs to update the gradient \(g\) at the given location \(x\) and return the value of the function being minimized, i.e., \(f(\mathbf x)\).

◆ connect_line_search_slot()

template<typename VectorType >
boost::signals2::connection SolverBFGS< VectorType >::connect_line_search_slot ( const std::function< Number(Number &f, VectorType &x, VectorType &g, const VectorType &p)> &  slot)

Connect a slot to perform a custom line-search.

Given the value of function f, the current value of unknown x, the gradient g and the search direction p, return the size \(\alpha\) of the step \(x \leftarrow x + \alpha p\), and update x, g and f accordingly.

◆ connect_preconditioner_slot()

template<typename VectorType >
boost::signals2::connection SolverBFGS< VectorType >::connect_preconditioner_slot ( const std::function< void(VectorType &g, const FiniteSizeHistory< VectorType > &s, const FiniteSizeHistory< VectorType > &y)> &  slot)

Connect a slot to perform a custom preconditioning.

The preconditioner is applied inside the two loop recursion to vector g using the history of position increments s and gradient increments y.

One possibility is to use the oldest s,y pair:

const auto preconditioner = [](VectorType & g,
if (s.size() > 0)
{
const unsigned int i = s.size() - 1;
const auto yy = y[i] * y[i];
const auto sy = s[i] * y[i];
Assert(yy > 0 && sy > 0, ExcInternalError());
g *= sy / yy;
}
};

No preconditioning is performed if the code using this class has not attached anything to the signal.

Member Data Documentation

◆ additional_data

template<typename VectorType >
const AdditionalData SolverBFGS< VectorType >::additional_data
protected

Additional data to the solver.

Definition at line 163 of file solver_bfgs.h.

◆ line_search_signal

template<typename VectorType >
boost::signals2::signal< Number(Number &f, VectorType &x, VectorType &g, const VectorType &p)> SolverBFGS< VectorType >::line_search_signal
protected

Signal used to perform line search.

Definition at line 170 of file solver_bfgs.h.

◆ preconditioner_signal

template<typename VectorType >
boost::signals2::signal<void(VectorType & g, const FiniteSizeHistory<VectorType> &s, const FiniteSizeHistory<VectorType> &y)> SolverBFGS< VectorType >::preconditioner_signal
protected

Signal used to perform preconditioning.

Definition at line 178 of file solver_bfgs.h.


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