# lbfgs.m

From Spinach Documentation Wiki

Calculates an approximation to the Newton-Raphson search direction using past gradients to build a serviceable substitute to a Hessian. The Hessian matrix is never explicitly formed or inverted. This function is the implementation from section 4 of http://dx.doi.org/10.1090/S0025-5718-1980-0572855-7

## Contents

## Syntax

direction=lbfgs(dx_hist,dg_hist,g)

## Arguments

dx_hist - history of x increments, a stack of column vectors, from the latest to the earliest dg_hist - history of gradient increments, a stack of column vectors, from the latest to the earliest g - current gradient

## Output

direction - LBFGS approximation to the search direction

## Notes

The L-BFGS algorithm is the default of fminnewton.m, and is a good mix of computational efficiency and fast convergence.

## See also

fminnewton.m, hessreg.m, linesearch.m

*Version 2.2, authors: Ilya Kuprov, David Goodwin*