LBFGS Class Reference

The LBFGS class defines a solver using LBFGS iteration method. More...

#include <LBFGS.hpp>

Collaboration diagram for LBFGS:

Public Member Functions
	LBFGS (const unsigned MH=10, const unsigned MI=500, const double AT=datum::eps, const double RT=datum::eps)
template<typename F > requires requires(F t, const vec& x) { { t.evaluate_residual(x) } -> std::same_as<vec>; { t.evaluate_jacobian(x) } -> std::same_as<mat>; }
int	optimize (F &func, vec &x)

Detailed Description

The LBFGS class defines a solver using LBFGS iteration method.

The LBFGS method is a rank two quasi–Newton method which has a super linear convergence rate. The LBFGS class supports both conventional BFGS and LBFGS method which uses limited history information.

\begin{gather} K_{n+1}^{-1}=\left(I-\dfrac{\Delta{}UR^T}{R^T\Delta{}U}\right)K_n^{-1}\left(I-\dfrac{R\Delta{}U^T}{R^T\Delta{}U}\right)+\dfrac{\Delta{}U\Delta{}U^T}{R^T\Delta{}U}. \end{gather}

The \(I\) is identity matrix. The \(\Delta{}U\) is current displacement increment. The \(R\) is current residual. For brevity, in both terms, the subscript \(n\) representing current step is dropped.

Author

tlc

Date

13/07/2022

Version

0.1.0

Constructor & Destructor Documentation

LBFGS()

LBFGS::LBFGS ( const unsigned  MH = 10, const unsigned  MI = 500, const double  AT = datum::eps, const double  RT = datum::eps  )

inlineexplicit

Member Function Documentation

optimize()

template<typename F >
requires requires(F t, const vec& x) { { t.evaluate_residual(x) } -> std::same_as<vec>; { t.evaluate_jacobian(x) } -> std::same_as<mat>; }

int LBFGS::optimize ( F &  func, vec &  x  )

inline

Here is the caller graph for this function:

---

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

• Toolbox/LBFGS.hpp