Numerical experience with limited-memory quasi-Newton and truncated Newton methods. (English) Zbl 0784.90086

Zou, X.; Navon, I. M.; Berger, M.; Phua, K. H.; Schlick, T.; Le Dimet, F. X.

SIAM J. Optim. 3, No. 3, 582-608 (1993).

Summary: 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. Hillstrom, ACM Trans. Math. Software 7, 17-41 (1981; Zbl 0454.65049)], 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 Ser. B 45, No. 3, 503-528 (1989; Zbl 0696.90048)] 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.

MSC:

90C30	Nonlinear programming
90-08	Computational methods for problems pertaining to operations research and mathematical programming
65K05	Numerical mathematical programming methods
93C20	Control/observation systems governed by partial differential equations
93C95	Application models in control theory
65K10	Numerical optimization and variational techniques
76B65	Rossby waves (MSC2010)
90C06	Large-scale problems in mathematical programming

Keywords:

synthetic cluster functions; limited-memory quasi-Newton; truncated Newton methods; unconstrained nonlinear optimization

Citations:

Zbl 0454.65049; Zbl 0696.90048

Software:

TNPACK; L-BFGS; minpack