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A stochastic method for global optimization. (English) Zbl 0525.90076


MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming
65K10 Numerical optimization and variational techniques
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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[1] F. Archetti, B. Betro and S. Steffe, ”A theoretical framework for global optimization via random sampling”, Tech. Rept., University of Pisa (1975).
[2] L. De Biase and F. Frontini, ”A stochastic method for global optimization: its structure and numerical performance”, in: L.C.W. Dixon and G.P. Szegö, eds.,Towards global optimisation 2 (North-Holland, Amsterdam, 1978) pp. 85–102. · Zbl 0396.90082
[3] L.C.W. Dixon and G.P. Szegö, eds.,Towards global optimisation (North-Holland, Amsterdam, 1975). · Zbl 0309.90052
[4] L.C.W. Dixon, J. Gomulka and G.P. Szegö, ”Towards global optimisation”, in: L.C.W. Dixon and G.P. Szegö, eds.,Towards global optimisation (North-Holland, Amsterdam, 1975) pp. 29–54.
[5] L.C.W. Dixon and G.P. Szegö, eds.,Towards global optimisation 2 (North-Holland, Amsterdam, 1978).
[6] L.C.W. Dixon and G.P. Szegö, ”The global optimisation problem: an introduction”, in: L.C.W. Dixon and G.P. Szegö, eds.,Towards global optimisation 2 (North-Holland, Amsterdam, 1978) pp. 1–18.
[7] W. Eberl and R. Hafner, ”Die asymptotische Verteilung von Koinzidenzen”,Zeitschrift für Wahrscheinlichkeitsrechnung 18 (1971) 322–332. · Zbl 0204.51403
[8] B. Everitt,Cluster analysis (Heinmann, London, 1974). · Zbl 0507.62060
[9] J. Gomulka, ”Two implementations of Branin’s method: Numerical experience”, in: L.C.W. Dixon and G.P. Szegö, eds.,Towards global optimisation 2 (North-Holland, Amsterdam, 1978) pp. 151–164. · Zbl 0407.90075
[10] L. De Haan, ”Estimation of the minimum of a function using order statistics”, Tech. Rept., Erasmus University, Rotterdam (1979).
[11] G. van der Hoek and M.W. Dijkshoorn, ”A numerical comparison of self scaling variable metric algorithms”, Tech. Rept., Erasmus University, Rotterdam (1979).
[12] A. Kester, ”Asymptotic normality of the number of small distances between random points in a cube”,Stochastic processes and their Applications 3 (1975) 45–54. · Zbl 0307.60021 · doi:10.1016/0304-4149(75)90005-8
[13] W.L. Price, ”A controlled random search procedure for global optimisation”, in: L.C.W. Dixon and G.P. Szegö, eds.,Towards global optimisation 2 (North-Holland, Amsterdam, 1978) pp. 71–84. · Zbl 0394.90092
[14] A.A. Törn, ”Cluster analysis using seed points and density-determined hyperspheres with an application to global optimization”,Proceedings of 3rd International Joint Conference on Pattern Recognition (IEEE Computer Society, Silver Spring, MD, 1976) pp. 394–398.
[15] A.A. Törn, ”Optimality by means of confidence”, Technical report, Åbo Swedish University School of Economics (1979).
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