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The solver works as follows:
 1.
 Choose , l, . Set k=0.
 2.
 Compute
 
(79) 
 (80) 
where meets the Wolfe conditions.
 3.
 Let =min, . Update times using the pairs
,
i.e., let
 

 
 (81) 
 
 (82) 
 4.
 Set k=k+1 and go to 2 if the residual power is not small enough.
The update is not formed explicitly; instead we compute
with an iterative formula
Nocedal (1980). Liu and Nocedal (1989) propose scaling the initial
symmetric positive definite at each iteration as follows:
 
(83) 
This scaling greatly improves the performances of the method.
Liu and Nocedal (1989) show that the storage limit for largescale problems
has little effects.
A common choice for l is l=5. In practice, the initial guess
for the Hessian is the identity matrix ;
then it might be scaled as proposed in equation (). The
nonlinear solver as detailed in the previous algorithm converges to
a local minimizer of .
Next: Minimizing the Huber function
Up: Algorithm for minimizing the
Previous: The limited memory BFGS
Stanford Exploration Project
5/5/2005