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Multiplicative Programming Problems

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Handbook of Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 2))

Abstract

This chapter reviews recent algorithmic developments in multiplicative programming. The multiplicative programming problem is a class of minimization problems containing a product of several convex functions either in its objective or in its constraints. It has various practical applications in such areas as microeconomics, geometric optimization, multicriteria optimization and so on. A product of convex functions is in general not (quasi)convex, and hence the problem can have multiple local minima. However, some types of multiplicative problems can be solved in a practical sense. The types to be discussed in this chapter are minimization of a product of p convex functions over a convex set, minimization of a sum of p convex multiplicative functions, and minimization of a convex function subject to a constraint on a product of p convex functions. If p is less than four or five, it is shown that parametric simplex algorithms or global optimization algorithms work very well for these problems.

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Author information

Authors and Affiliations

  1. Institute of Human and Social Sciences, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan

    Hiroshi Konno

  2. Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan

    Takahito Kuno

Authors
  1. Hiroshi Konno
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  2. Takahito Kuno
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Trier, Trier, Germany

    Reiner Horst

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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© 1995 Springer Science+Business Media Dordrecht

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Konno, H., Kuno, T. (1995). Multiplicative Programming Problems. In: Horst, R., Pardalos, P.M. (eds) Handbook of Global Optimization. Nonconvex Optimization and Its Applications, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2025-2_8

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  • DOI: https://doi.org/10.1007/978-1-4615-2025-2_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5838-1

  • Online ISBN: 978-1-4615-2025-2

  • eBook Packages: Springer Book Archive

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