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A C++ Class Library for Interval Arithmetic in Global Optimization

  • Chapter
State of the Art in Global Optimization

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

Abstract

Global optimization methods based on interval arithmetic have potential to efficiently solve problems that standard nonlinear programming techniques cannot handle well. In interval arithmetic the machine arithmetic is performed by approximating a real number with an enclosing interval, rather than with a single floating point number. Hence, an automatic control over rounding errors is provided. To use interval arithmetic in practice either a language with built-in interval arithmetic or a suitable subroutine library is needed. Such a library can with advantage be implemented in C++, realizing intervals as objects with well defined interfaces. In this paper we report experience from implementing and using a C++ class library for global optimization using interval arithmetic. Measurements show that the use of object oriented programming and operator overloading does not affect performance negatively. In fact, our C++ implementation of interval arithmetic is actually faster than a comparable Fortran implementation.

This work has partially been supported by the Center for Industrial Information Technology (CENIIT).

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Author information

Authors and Affiliations

  1. Division of Optimization, Department of Mathematics, Linköping University, S-581 83, Linköping, Sweden

    Kristina Holmqvist & Athanasios Migdalas

Authors
  1. Kristina Holmqvist
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  2. Athanasios Migdalas
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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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Holmqvist, K., Migdalas, A. (1996). A C++ Class Library for Interval Arithmetic in Global Optimization. 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_14

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  • DOI: https://doi.org/10.1007/978-1-4613-3437-8_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3439-2

  • Online ISBN: 978-1-4613-3437-8

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