LBFGS (Release A)

Large-scale unconstrained minimization

The method implemented in LBFGS is the limited-memory BFGS algorithm, as described Liu and Nocedal [1989]. It is intended for problems with many variables. In this method quasi-Newton corrections are stored in vector form; when the available storage is used up, the oldest correction is deleted to make space for a new one. The user specifies the number m of BFGS corrections that should be stored. LBFGS requires 2m(n+1)+4n storage locations.

The steplength is determined at each iteration by a line-search routine (supplied by J. Moré and D. Thuente) that enforces a sufficient decrease condition and a curvature condition.

LBFGS is written in Fortran 77. Single- and double-precision versions of the software are available. Machine dependencies are restricted to BLOCK DATA LB2.

LBFGS is also available in the Harwell Library under the name VA15.

Need more info?

Contact:

Jorge Nocedal
Northwestern University
Department of Electric Engineering and Computer Science
Evanston, IL 60208
Phone: (708) 491-5038 
E-Mail: nocedal@eecs.nwu.edu

Reference:

D. C. Liu and J. Nocedal, On the limited memory BFGS method for large-scale optimization, Math. Programming 45 (1989), pp. 503--528.

J. Nocedal, Updating quasi-Newton matrices with limited storage, Math. Comp. 24 (1980), pp. 773--782.

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