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Global Optimization: Cutting Angle Method

  • Reference work entry
Encyclopedia of Optimization

  • 166 Accesses

Article Outline

Introduction

Definitions

  Notation

  Abstract Convex Functions

  IPH Functions

  Lipschitz Functions

Methods

  Generalized Cutting Plane Method

  Global Minimization of IPH Functions over Unit Simplex

  Global Minimization of Lipschitz Functions

  The Auxiliary Problem

  Solution of the Auxiliary Problem

Conclusions

References

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Notes

  1. 1.

    The norm \( ||\cdot|| \) can be replaced by any metric, or, more generally, any distance function based on Minkowski gauge. For example, a polyhedral distance \( d_P(x,y)=\max \{[(x-y), h_i]\; | 1\leq i \leq m \} \), where \( h_i \in \mathbb{R}^n, i=1,\ldots,m \) is the set of vectors that define a finite polyhedron \( P=\bigcap_{i=1}^m \{x\;|\; [x , h_i] \leq 1 \} \).

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Author information

Authors and Affiliations

  1. Centre for Informatics and Applied Optimization, School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia

    Adil Bagirov

  2. School of Engineering and Information Technology, Deakin University, Victoria, Australia

    Gleb Beliakov

Authors
  1. Adil Bagirov
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  2. Gleb Beliakov
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Bagirov, A., Beliakov, G. (2008). Global Optimization: Cutting Angle Method . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_229

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