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Multiobjective Duality for Convex-Linear Problems

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Operations Research Proceedings 1999

Part of the book series: Operations Research Proceedings 1999 ((ORP,volume 1999))

Summary

We consider a general vector minimum optimization problem with convex objective functions and linear inequality constraints.

By means of linear scalarization and using the Fenchel-Rockafellar duality approach for the scalarized problem there is constructed a multiobjective dual maximum problem.

The investigations are devoted to weak and strong duality assertions. Moreover, optimality conditions are verified for properly efficient and efficient solutions.

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References

  1. Jahn, J., Duality in vector optimization. Math. Programming 25, 1983, 343–353.

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  2. Luc, D. T., Theory of Vector Optimization. Lecture Notes in Econom. and Math. Systems 319, Springer, Berlin, 1989.

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  3. Sawaragi, Y., Nakayama, H. and Tanino, T., Theory of Multiobjective Optimization. Academic Press, New York, 1985.

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  4. Song, W., Duality in set-valued optimization. Polish Academy of Science, Warsaw, 1998.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Technical University Chemnitz, Germany

    Gert Wanka & Radu-Ioan Bot

Authors
  1. Gert Wanka
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  2. Radu-Ioan Bot
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Editor information

Editors and Affiliations

  1. Fakultät für Wirtschaftswissenschaft, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, D-39106, Magdeburg, Germany

    Karl Inderfurth  & Gerhard Schwödiauer  & 

  2. Fachbereich Rechts- und Wirtschaftswissenschaften, Technische Universität Darmstadt, Hochschulstr. 1, D-64289, Darmstadt, Germany

    Wolfgang Domschke

  3. Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, D-39106, Magdeburg, Germany

    Friedrich Juhnke

  4. Wirtschaftswissenschaftliche Fakultät, Universität Passau, Innstr. 29, D-90030, Passau, Germany

    Peter Kleinschmidt

  5. Wirtschaftswissenschaftliche Fakultät, Martin-Luther-Universität Halle-Wittenberg, Große Steinstr. 73, D-06108, Halle/Saale, Germany

    Gerhard Wäscher

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© 2000 Springer-Verlag Berlin Heidelberg

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Wanka, G., Bot, RI. (2000). Multiobjective Duality for Convex-Linear Problems. In: Inderfurth, K., Schwödiauer, G., Domschke, W., Juhnke, F., Kleinschmidt, P., Wäscher, G. (eds) Operations Research Proceedings 1999. Operations Research Proceedings 1999, vol 1999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58300-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-58300-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67094-0

  • Online ISBN: 978-3-642-58300-1

  • eBook Packages: Springer Book Archive

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