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Accelerating Convergence of Branch-and-Bound Algorithms For Quadratically Constrained Optimization Problems

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State of the Art in Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 7))

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Abstract

We consider methods for finding global solutions to quadratically constrained programs. We present a branch-and-bound algorithm which solves a sequence of linear programs, each of which approximates the original problem over a hyperrectangular region. Tightening the bounds produces arbitrarily tight approximations as the volume of the hyperrectangle decreases. Computational experiments are given which relate the efficiency of the algorithm to the input parameters. In order to reduce the amount of work necessary to isolate global solutions within a small region, local optimization techniques are embedded within the branch-and-bound scheme. In particular, the use of the interval Newton method applied to the KKT system is discussed and shown to be computationally beneficial. Extensions are considered which allow the branch-and- bound algorithm to process more general nonlinear functions than quadratic.

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Author information

Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Tim Van Voorhis & Faiz Al-Khayyal

Authors
  1. Tim Van Voorhis
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  2. Faiz Al-Khayyal
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Editor information

Editors and Affiliations

  1. Princeton University, USA

    C. A. Floudas

  2. University of Florida, USA

    P. M. Pardalos

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© 1996 Kluwer Academic Publishers

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Van Voorhis, T., Al-Khayyal, F. (1996). Accelerating Convergence of Branch-and-Bound Algorithms For Quadratically Constrained Optimization Problems. In: Floudas, C.A., Pardalos, P.M. (eds) State of the Art in Global Optimization. Nonconvex Optimization and Its Applications, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3437-8_18

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  • DOI: https://doi.org/10.1007/978-1-4613-3437-8_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3439-2

  • Online ISBN: 978-1-4613-3437-8

  • eBook Packages: Springer Book Archive

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