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Numerical Experience with Limited-Memory Quasi-Newton and Truncated Newton
Methods

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Computational experience with several limited-memory quasi-Newton and truncated
Newton methods for unconstrained nonlinear optimization is described. Comparative
tests were conducted on a well known test library [J. J. Moré, B.
S. Garbow, and K.E. Hillstorm, *ACM Trans. Math. Software* 7 (1981),
pp. 17-41], on several synthetic problems allowing control of the clustering
of eigenvalues in the Hessian spectrum, and on some large-scale problems
in oceanography and meteorology. The results indicate that among the tested
limited-memory quasi-Newton methods, the L-BFGS method [D.C. Liu and J.
Nocedal, *Math. Programming,* 45 (1989) pp. 503-528] has the
best overall performance for the problems examined. The numerical performance
of two truncated Newton methods, differing in the inner-loop solution for
the search vector, is competitive with that of L-BFGS.

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