Difference between revisions of "Lbfgs.m"

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(See also)
(Returns)
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                       use for the Hessian estimate
 
                       use for the Hessian estimate
  
==Returns==
+
==Output==
  
 
     direction      - LBFGS approximation to the  
 
     direction      - LBFGS approximation to the  

Revision as of 16:29, 13 August 2018

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,n_grads)

Arguments

   dx_hist         - history of x increments,
                     bookshelf array

   dg_hist         - history of gradient increments,
                     bookshelf array

   g               - current gradient

   n_grads         - max number of past gradients to 
                     use for the Hessian estimate

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