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Optimization and Related Topics pp 15–26Cite as

An Exact Method for Solving the Subproblem of the Cutting Angle Method of Global Optimization

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Part of the book series: Applied Optimization ((APOP,volume 47))

Abstract

An exact method for solving the subproblem of the cutting angle method of global optimization for problems of minimizing increasing positively homogeneous of degree one functions is presented. The approach can be used to develop algorithms for solving the subproblems when solving some broader classes of problems by the cutting angle method.

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References

  • Andramonov, M.Yu., Rubinov, A.M. and Glover, B. (1997), Cutting angle method for minimizing increasing convex along rays functions, Research Report 97/7, University of Ballarat, Australia.

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  • Andramonov, M.Yu., Rubinov, A.M. and Glover, B. (1999), Cutting angle method in global optimization, Applied Mathematics Letters, Vol. 12, 95100.

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  • Bagirov, A.M. and Rubinov, A.M. (2000), Global minimization of increasing positively homogeneous functions over unit simplex, Annals of Operations Research, to appear.

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  • Rubinov, A.M. and Andramonov, M.Yu. (1999a), Minimizing increasing star-shaped functions based on abstract convexity, Journal of Global Optimization, Vol. 15, 19–39.

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  • Rubinov, A.M. and Andramonov, M.Yu. (1999b), Lipschitz programming via increasing convex along rays functions, Optimization Methods and Software, Vol. 10, 763–781.

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Author information

Authors and Affiliations

  1. US WEST Advanced Technologies, 4001 Discovery Drive, Boulder, CO, 80303, USA

    Djangir A. Babayev

Authors
  1. Djangir A. Babayev
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Editor information

Editors and Affiliations

  1. School of Information Technology & Mathematical Sciences, University of Ballarat, Victoria, Australia

    Alexander Rubinov

  2. School of Mathematics and Statistics, Curtin University of Technology, WA, Australia

    Barney Glover

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© 2001 Springer Science+Business Media Dordrecht

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Babayev, D.A. (2001). An Exact Method for Solving the Subproblem of the Cutting Angle Method of Global Optimization. In: Rubinov, A., Glover, B. (eds) Optimization and Related Topics. Applied Optimization, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6099-6_2

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  • DOI: https://doi.org/10.1007/978-1-4757-6099-6_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4844-1

  • Online ISBN: 978-1-4757-6099-6

  • eBook Packages: Springer Book Archive

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