Unconstrained Optimization Packages

LBFGS Author Jorge Nocedal
Northwestern University
Department of Electric Engineering and Computer Science
Evanston, IL 60208
Phone: (708) 491-5038
E-mail: nocedal@ece.nwu.edu
Language FORTRAN
Algorithm limited-memory BFGS algorithm
Input Format
Modeling Languages link
Commercial Status free
Platform Any machine with a reasonable amount of memory and a Fortran compiler
Remarks 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.
  • 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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