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Reference documentation for deal.II version 9.2.0
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Reference documentation for deal.II version 9.2.0
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#include <deal.II/optimization/solver_bfgs.h>
Classes | |
| struct | AdditionalData |
Public Types | |
| using | Number = typename VectorType::value_type |
 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 ¤t_iterate)> &slot) |
| Public Member Functions inherited from Subscriptor | |
| Subscriptor () | |
| Subscriptor (const Subscriptor &) | |
| Subscriptor (Subscriptor &&) noexcept | |
| virtual | ~Subscriptor () |
| Subscriptor & | operator= (const Subscriptor &) |
| Subscriptor & | operator= (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 ¤t_iterate), StateCombiner > | iteration_status |
Additional Inherited Members | |
| Static Public Member Functions inherited from Subscriptor | |
| static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
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 58 of file solver_bfgs.h.
| using SolverBFGS< VectorType >::Number = typename VectorType::value_type |
Number type.
Definition at line 64 of file solver_bfgs.h.
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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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Additional data to the solver.
Definition at line 165 of file solver_bfgs.h.
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Signal used to perform line search.
Definition at line 172 of file solver_bfgs.h.
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Signal used to perform preconditioning.
Definition at line 180 of file solver_bfgs.h.
1.8.17