×

zbMATH — the first resource for mathematics

The barrier attribute of filled functions. (English) Zbl 1043.90070
Summary: A number of filled functions was proposed recently. This paper presents a new perspective of the filled functions: their barrier attribute. More filled functions can be constructed according to this new interpretation. Two of them are with finite barriers while the remains are with infinite barriers.

MSC:
90C26 Nonconvex programming, global optimization
90C51 Interior-point methods
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Carroll, C., The created response surface technique for optimization nonlinear restrained systems, Operations research, 9, 169-184, (1961) · Zbl 0111.17004
[2] Fiacco, A.; McCormick, G., Nonlinear programming: sequential unconstrained minimization techniques, (1968), John Wiley New York · Zbl 0193.18805
[3] Ge, R.; Qin, Y., A class of filled functions for finding global minimizers of a function of several variables, Journal of optimization theory and applications, 54, 241-252, (1987) · Zbl 0595.65072
[4] Ge, R., A filled function method for finding a global minimizer of a function of several variables, Mathematical programming, 46, 191-204, (1990) · Zbl 0694.90083
[5] Horst, R.; Tuy, H., Global optimization (deterministic approaches), (1996), Springer-Verlag Berlin · Zbl 0867.90105
[6] Levy, A.; Montalvo, A., The tunneling algorithm for the global minimization of functions, SIAM journal on scientific and statistical computing, 6, 15-29, (1985) · Zbl 0601.65050
[7] Liu, X., Several filled functions with mitigators, Appl. math. and comput., 133, 375-385, (2002) · Zbl 1135.90372
[8] X. Liu, Two new classes of filled functions, Applied Mathematics and Computation, submitted for publication · Zbl 1053.90120
[9] Pintér, J., Global optimization in action, (1996), Kluwer Dordrecht
[10] Törn, A.; Žilinskas, A., Global optimization, (1989), Springer-Verlag Berlin · Zbl 0752.90075
[11] Vicente, L.; Calamai, P., Bilevel and multilevel programming: a bibliography review, Journal of global optimization, 5, 291-306, (1994) · Zbl 0822.90127
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.