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Topics in global optimization

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Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 909))

Abstract

A summary of the reserch done in global optimization at the Numerical Analysis Departament of IIMAS-UNAM is given. The concept of the Tunnelling Function and the key ideas of the Tunnelling Algorithm as applied to Unconstrained Global Optimization, Stabilization of Newton's Method and Constrained Global Optimization are presented. Numerical results for several examples are given, they have from one to ten variables and from three to several thousands of local minima, clearly illustrating the robustness of the Tunnelling Algorithm.

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References

  1. A. V. Levy and A. Montalvo, “The Tunnelling Algorithm for the Global Minimization of Functions”, Dundee Biennal Conference on Numerical Analysis, Univ. of Dundee, Scotland, 1977.

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  2. A. V. Levy and A. Montalvo, “Algoritmo de Tunelizacion para la Optimacion Global de Funciones”, Comunicaciones Tecnicas, Serie Naranja, No. 204, IIMAS-UNAM, Mexico D. F., 1979.

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  3. A. V. Levy and A. Calderon, “A Robust Algorithm for Solving Systems of Non-linear Equations”, Dundee Biennal Conference on Numerical Analysis, Univ. of Dundee, Scotland, 1979.

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  4. A. Calderon, “Estabilization del Metodo de Newton para la Solucion de Sistemas de Ecuaciones No-Lineales,” B. Sc. Thesis, Mathematics Dept. UNAM, Mexico D.F., 1978.

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  5. A. V. Levy and A. Montalvo, “A Modification to the Tunnelling Algorithm for Finding the Global Minima of an Arbitrary One Dimensional Function”, Comunicaciones Tecnicas, Serie Naranja, No. 240, IIMAS-UNAM, 1980.

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  6. D. M. Himmelblau, “Applied Nonlinear Programing,” Mc Graw-Hill Book Co. N. Y., 1972.

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Authors and Affiliations

  1. IIMAS-UNAM, Mexico 20, D.F., A.P. 20-726, Mexico City, Mexico

    A. V. Levy, A. Montalvo, S. Gomez & A. Calderon

Authors
  1. A. V. Levy
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  2. A. Montalvo
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  3. S. Gomez
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  4. A. Calderon
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Editor information

J. P. Hennart

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© 1982 Springer-Verlag

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Levy, A.V., Montalvo, A., Gomez, S., Calderon, A. (1982). Topics in global optimization. In: Hennart, J.P. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 909. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092957

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  • DOI: https://doi.org/10.1007/BFb0092957

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11193-1

  • Online ISBN: 978-3-540-38986-6

  • eBook Packages: Springer Book Archive

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