Difference between revisions of "Lbfgs.m"

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{{DISPLAYTITLE:lbfgs.m}}
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{{DISPLAYTITLE:lbfgs.m}} __NOTOC__
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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
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This function calculates the quasi-Newton update with the gradient history, giving the search direction. Based on the [[quasinewton.m|BFGS]] algorithm, this limited-memory BFGS (L-BFGS) algorithm stores only few vectors that implicitly represent the approximation of the BFGS algorithm (which stores a matrix equal to the number of optimisation variables)
 
  
 
==Syntax==
 
==Syntax==
  
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     direction=lbfgs(x_hist,df_hist,grad,N)
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     direction=lbfgs(dx_hist,dg_hist,g)
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==Description==
 
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This function is the implementation from section 4 of http://dx.doi.org/10.1090/S0025-5718-1980-0572855-7
 
  
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==Arguments==
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==Parameters==
 
              
 
              
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    x_hist         - vector array of waveform history, num_var x size_store
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    dx_hist         - history of x increments, a stack
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                      of column vectors, from the latest
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    df_hist        - vector array of gradient history, num_var x size_store
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                      to the earliest
 
   
 
   
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    grad          - vector of the current gradient, (num_vars x 1)
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    dg_hist        - history of gradient increments,
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                      a stack of column vectors, from
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                      the latest to the earliest
 
   
 
   
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    N              - number of waveform/gradient vectors to store (default=20)
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    g              - current gradient
  
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==Returns==
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==Output==
  
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    direction     - the vector giving the BFGS approximation to the search direction
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    direction       - LBFGS approximation to the  
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                      search direction
  
 
==Notes==
 
==Notes==
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The L-BFGS algorithm is the default of [[fminnewton.m]], and should be considered a good mix of computational efficiency and fast convergence.
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The L-BFGS algorithm is the default of [[Fmaxnewton.m]], and is a good mix of computational efficiency and fast convergence.
  
 
==See also==
 
==See also==
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[[quasinewton.m]], [[fminnewton.m]], [[optim_tols.m]]
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[[fmaxnewton.m]], [[hessreg.m]], [[bracketing.m]], [[sectioning.m]], [[bfgs_upd.m]], [[Optimal_control_module]]
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''Revision 3284, authors: [[Ilya Kuprov]] [[David Goodwin]]''
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''Version 2.2, authors: [[Ilya Kuprov]], [[David Goodwin]]''

Latest revision as of 19:38, 6 June 2026

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)

Parameters

   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, bfgs_upd.m, Optimal_control_module

Version 2.2, authors: Ilya Kuprov, David Goodwin

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