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

Abstract

Computational experience with several limited-memory quasi-Newton and trun- cated Newton methods for unconstrained nonlinear optimization is described. Comparative tests were conducted on a well-known test library (J. J. Mor, B. S. Garbow, and K. E. Hillstrom, 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.