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lbfgs is an implementation of the L-BFGS algorithm [1] to solve 
unconstrained minimization problems via a limited-memory quasi-Newton (BFGS) 
algorithm. It is called a limited-memory method because a low-rank 
approximation of the Hessian matrix inverse is stored instead of the entire 
Hessian inverse. The program was originally written in Fortran [2] by Jorge 
Nocedal, incorporating some functions originally written by Jorge J. Moré 
and David J. Thuente, and translated into Lisp automatically via the program 
f2cl. The Maxima package lbfgs comprises the translated code 
plus an interface function which manages some details.
References:
[1] D. Liu and J. Nocedal. "On the limited memory BFGS method for large scale optimization". Mathematical Programming B 45:503–528 (1989)
[2] http://netlib.org/opt/lbfgs_um.shar
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