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On Finiteness of Modified Beale’s Algorithm for Solving Nonconvex Quadratic Program

  • Conference paper
Operations Research Proceedings 1994

Part of the book series: Operations Research Proceedings ((ORP,volume 1994))

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Summary

The paper deals with Beale’s method, which is generalized for calculating a local minimum of any quadratic objective function subject to linear constraints. A theoretical background of the algorithm is given briefly and the finiteness of the procedure is proved. Solving of degenerate problems is mentioned.

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References

  1. Beale, E. M. L.: On Minimizing a Convex Function Subject to Linear inequalities J. Roy. Statist. Soc. 17, 173–184 (1955).

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  3. Abadie, J.: Nonlinear Programming. North Holland, Amsterdam, 1967.

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  4. Mráz, F.: Generalization of Beale’s Method for Solving Quadratic Programming Problem (thesis, in Czech). Faculty of Math, and Physics, Charles university, Prague, 1–55 (1976).

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  5. Mráz, F.: Local Minimizer of a Nonconvex Quadratic Programming problem. Computing 45, 283–289 (1990).

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  6. Nožička, F., Guddat, J., Hollatz, H.: Theorie der linearen Optimierung. Verlag, Berlin, 1972.

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  7. Väliaho, H.: Cycling Can Occur in Mräz’s Algorithm for Nonconvex Quadratic Programming. Computing 51, 183–184 (1993).

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Author information

Authors and Affiliations

  1. České Budějovice, Czech Republic

    František Mráz

Authors
  1. František Mráz
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Editor information

Editors and Affiliations

  1. Wirtschaftsinformatik und Operations Research, Universität zu Köln, Pohligstraße 1, D-50969, Köln, Germany

    Ulrich Derigs (Lehrstuhl) (Lehrstuhl)

  2. Mathematisches Institut, Universität zu Köln, Weyertal 80, D-50931, Köln, Germany

    Achim Bachem

  3. Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, D-24118, Kiel, Germany

    Andreas Drexl

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© 1995 Springer-Verlag Berlin Heidelberg

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Mráz, F. (1995). On Finiteness of Modified Beale’s Algorithm for Solving Nonconvex Quadratic Program. In: Derigs, U., Bachem, A., Drexl, A. (eds) Operations Research Proceedings 1994. Operations Research Proceedings, vol 1994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79459-9_12

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  • DOI: https://doi.org/10.1007/978-3-642-79459-9_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58793-4

  • Online ISBN: 978-3-642-79459-9

  • eBook Packages: Springer Book Archive

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