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Multicriteria Decision Making pp 37–68Cite as

Theory of Vector Maximization: Various Concepts of Efficient Solutions

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Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 21))

Abstract

This chapter introduces the basic concepts of vector optimization. After the discussion of a simple example from structural engineering partial orderings on ℝm are defined and connections to convex cones are investigated. Then we present the definitions of several variants of the efficiency notion: weak, proper, strong and essential efficiency. Relationships between these different concepts are investigated and simple examples illustrate these notions The last section is devoted to the scalarization of vector optimization problems. Based on various concepts of monotonicity basic scalarization results are described and the weighted sum approach is investigated in detail.

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Authors
  1. Johannes Jahn
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Editors and Affiliations

  1. Fern Universität, Hagen, Germany

    Tomas Gal  & Thomas Hanne  & 

  2. University of Cape Town, Rep. of South Africa

    Theodor J. Stewart

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© 1999 Springer Science+Business Media New York

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Jahn, J. (1999). Theory of Vector Maximization: Various Concepts of Efficient Solutions. In: Gal, T., Stewart, T.J., Hanne, T. (eds) Multicriteria Decision Making. International Series in Operations Research & Management Science, vol 21. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5025-9_2

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  • DOI: https://doi.org/10.1007/978-1-4615-5025-9_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7283-7

  • Online ISBN: 978-1-4615-5025-9

  • eBook Packages: Springer Book Archive

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