Lbfgs.m

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

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 Fmaxnewton.m, and is a good mix of computational efficiency and fast convergence.

See also

fmaxnewton.m, hessreg.m, bracketing.m, sectioning.m

Version 2.2, authors: Ilya Kuprov, David Goodwin