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Theory of Vector Optimization

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Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 52))

Abstract

We introduce several solution concepts for multicriteria optimization problems, give a characterization of approximately efficient elements and discuss a general scalarization procedure. Furthermore, we derive necessary and sufficient optimality conditions, a minimal point theorem, a vector-valued variational principle of Ekeland’s type, Lagrangean multiplier rules and duality statements. An overview on vector variational inequalities and vector equilibria is given. Moreover, we discuss the results for special classes of vector optimization problems (vector-valued location and approximation problems, multicriteria fractional programming and optimal control problems).

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  1. Department of Mathematics and Computer Science, D-06099, Halle an der Saale, Germany

    Christiane Tammer & Alfred Göpfert

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  1. University of Auckland, New Zealand

    Matthias Ehrgott

  2. Université de Valenciennes, France

    Xavier Gandibleux

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Tammer, C., Göpfert, A. (2003). Theory of Vector Optimization. In: Ehrgott, M., Gandibleux, X. (eds) Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. International Series in Operations Research & Management Science, vol 52. Springer, Boston, MA. https://doi.org/10.1007/0-306-48107-3_1

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