Ge, R. P.; Qin, Y. F. A class of filled functions for finding global minimizers of a function of several variables. (English) Zbl 0595.65072 J. Optimization Theory Appl. 54, 241-252 (1987). This paper is concerned with the filled function methods for finding global minimizers of a function of several variables. A class of filled functions are defined. The advantages and disadvantages of every filled function in the class are analyzed. The best one in this class is pointed out. The idea of how to construct a better filled function is given and employed to construct the class of filled functions. A method is also explored as how to locate minimizers or saddle points of a filled function only through the use of the gradient of a function. Cited in 65 Documents MSC: 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming Keywords:filled function methods; global minimizers; region of attraction PDFBibTeX XMLCite \textit{R. P. Ge} and \textit{Y. F. Qin}, J. Optim. Theory Appl. 54, 241--252 (1987; Zbl 0595.65072) Full Text: DOI References: [1] Ge, R. P.,A Filled Function Method for Finding a Global Minimizer of a Function of Several Variables, Paper Presented at the Dundee Biennial Conference on Numerical Analysis, Dundee, Scotland, 1983. [2] Ge, R. P.,The Theory of the Filled Function Method for Finding a Global Minimizer of a Nonlinearly Constrained Minimization Problem, Paper Presented at the SIAM Conference on Numerical Optimization, Boulder, Colorado, 1984. [3] Branin, F. H.,Solution of Nonlinear DC Network Problem via Differential Equations, Paper Presented at the IEEE International Conference on System Networks and Computers, Caxtepex, Mexico, 1971. [4] Branin, F. H., andHoo, S. K.,A Method for Finding Multiple Extrema of a Function of n Variables, Numerical Methods of Nonlinear Optimization, Edited by F. Lootsma, Academic Press, New York, New York, 1972. · Zbl 0271.65035 [5] Dixon, L. C. W., Gomulka, J., andSzeg?, G. P.,Toward a Global Optimization Technique, Toward Global Optimization, Edited by L. C. W. Dixon and G. P. Szego, North-Holland, Amsterdam, Holland, 1975. · Zbl 0309.90052 [6] Dixon, L. C. W., Gomulka, J., andHerson, S. E.,Reflections on the Global Optimization Problem, Optimization in Action, Edited by L. C. W. Dixon, Academic Press, New York, New York, 1976. [7] Goldstein, A. A., andPrice, J. F.,On Descent from a Local Minimum, Mathematics of Computation, Vol. 25, pp. 569-574, 1971. · Zbl 0223.65020 [8] Levy, A. V.,The Tunneling Algorithm for the Global Minimization of Functions, Paper Presented at the Dundee Biennial Conference on Numerical Analysis, Dundee, Scotland, 1977. [9] Levy, A. V.,The Tunneling Method Applied to Global Optimization, Paper Presented at the SIAM Conference on Numerical Optimization, Boulder, Colorado, 1984. [10] Shubert, B. O.,A Sequential Method Seeking the Global Minimum of a Function, SIAM Journal on Numerical Analysis, Vol. 9, pp. 379-388, 1972. · Zbl 0251.65052 [11] Szeg?, G. P.,Numerical Methods for Global Minimization, Proceedings of the IFAC Conference, Boston, Massachusetts, 1975. [12] Treccani, G., Trabattoni, L., andSzeg?, G. P.,A Numerical Method for the Isolation of Minima, Minimization Algorithms, Edited by G. P. Szeg?, Academic Press, New York, New York, 1972. 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.