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Reference documentation for deal.II version 9.4.1
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Reference documentation for deal.II version 9.4.1
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#include <deal.II/optimization/solver_bfgs.h>
Classes | |
| struct | AdditionalData |
Public Types | |
| using | Number = typename VectorType::value_type |
| 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) |
| boost::signals2::connection | connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType ¤t_iterate)> &slot) |
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 |
| GrowingVectorMemory< VectorType > | static_vector_memory |
| VectorMemory< VectorType > & | memory |
| boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType ¤t_iterate), StateCombiner > | iteration_status |
Subscriptor functionality | |
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class. | |
| 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) |
| using | map_value_type = decltype(counter_map)::value_type |
| using | map_iterator = decltype(counter_map)::iterator |
| std::atomic< unsigned int > | counter |
| std::map< std::string, unsigned int > | counter_map |
| std::vector< std::atomic< bool > * > | validity_pointers |
| const std::type_info * | object_info |
| static std::mutex | mutex |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
| void | check_no_subscribers () const noexcept |
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.
Definition at line 56 of file solver_bfgs.h.
| using SolverBFGS< VectorType >::Number = typename VectorType::value_type |
Number type.
Definition at line 62 of file solver_bfgs.h.
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inherited |
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explicit |
Constructor.
| 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., \(f(\mathbf x)\).
| 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.
| 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:
No preconditioning is performed if the code using this class has not attached anything to the signal.
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inherited |
Connect a function object that will be called periodically within iterative solvers. This function is used to attach monitors to iterative solvers, either to determine when convergence has happened, or simply to observe the progress of an iteration. See the documentation of this class for more information.
| slot | A function object specified here will, with each call, receive the number of the current iteration, the value that is used to check for convergence (typically the residual of the current iterate with respect to the linear system to be solved) and the currently best available guess for the current iterate. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated. The function object must return a SolverControl::State value that indicates whether the iteration should continue, has failed, or has succeeded. The results of all connected functions will then be combined to determine what should happen with the iteration. |
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protected |
Additional data to the solver.
Definition at line 163 of file solver_bfgs.h.
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protected |
Signal used to perform line search.
Definition at line 170 of file solver_bfgs.h.
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protected |
Signal used to perform preconditioning.
Definition at line 178 of file solver_bfgs.h.
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mutableprotectedinherited |
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protectedinherited |
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protectedinherited |
A signal that iterative solvers can execute at the end of every iteration (or in an otherwise periodic fashion) to find out whether we should continue iterating or not. The signal may call one or more slots that each will make this determination by themselves, and the result over all slots (function calls) will be determined by the StateCombiner object.
The arguments passed to the signal are (i) the number of the current iteration; (ii) the value that is used to determine convergence (oftentimes the residual, but in other cases other quantities may be used as long as they converge to zero as the iterate approaches the solution of the linear system); and (iii) a vector that corresponds to the current best guess for the solution at the point where the signal is called. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated.
1.9.5