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On the Relations Between Different Dual Problems in Convex Mathematical Programming

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Book cover Operations Research Proceedings 2001

Part of the book series: Operations Research Proceedings 2001 ((ORP,volume 2001))

Abstract

Using the Fenchel-Rockafellar approach for the convex mathematical programming problem with inequality constraints different dual optimization problems by means of distinct perturbations of the primal problem are derived and studied. The classical Lagrange dual problem is one of those dual problems obtained by the perturbation of the right hand side of the inequality constraints. For the various dual problems equality/inequality relations between the optimum values are verified under appropriate assumptions. Moreover, the duality relations to the primal problem are considered, in particular strong duality. Using the dual problems some optimality conditions are established.

The results are illustrated by some examples.

The application and usefulness for the construction of general multiobjective dual problems to the general multiobjective convex optimization problem is mentioned.

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References

  1. Ekeland I., Temam R. (1976) Convex analysis and variational problems. North-Holland Publishing Company, Amsterdam

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  2. Elster K.-H., Reinhardt R., Schäuble M., Donath G. (1977) Einführung in die nichtlineare Optimierung. Teubner, Leipzig

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  3. Rockafellar R.T. (1970) Convex Analysis. Princeton University Press, Princeton, NJ

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  4. Wanka G., Boţ R.-I. (2001) A new duality approach for multiobjective convex optimization problems. Fakultät für Mathematik, TU Chemnitz, Preprint 2001–6

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Technology Chemnitz, Germany

    Gert Wanka & Radu-Ioan Boţ

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

Editors and Affiliations

  1. Fakultät 3, Institut für Logistik und Informationsmanagement, Lehrstuhl für Wirtschaftsinformatik und Operations Research, Gerhard-Mercator-Universität Duisburg, Lotharstraße 63, 47057, Duisburg, Germany

    Peter Chamoni

  2. Fakultät 3, Institut für Logistik und Informationsmanagement, Lehrstuhl für Produktionswirtschaft und Industriebetriebslehre, Gerhard-Mercator-Universität Duisburg, Lotharstraße 63, 47057, Duisburg, Germany

    Rainer Leisten

  3. Fachbreich Mathematik · Fachgebiet Diskrete Optimierung, Technische Universität Darmstadt, Schlossgartenstraße 7, 64289, Darmstadt, Germany

    Alexander Martin

  4. WestLB · Abteilung Mathematik/Operations Research, Herzogstraße 15, 40217, Düsseldorf, Germany

    Joachim Minnemann

  5. Institut für Betriebswirtschaftslehre · Fachgebiet Fertigungs- und Materialwirtschaft, Technische Universität Darmstadt, Hochschulstraße 1, 64289, Darmstadt, Germany

    Hartmut Stadtler

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© 2002 Springer-Verlag Berlin Heidelberg

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Wanka, G., Boţ, RI. (2002). On the Relations Between Different Dual Problems in Convex Mathematical Programming. In: Chamoni, P., Leisten, R., Martin, A., Minnemann, J., Stadtler, H. (eds) Operations Research Proceedings 2001. Operations Research Proceedings 2001, vol 2001. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50282-8_32

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  • DOI: https://doi.org/10.1007/978-3-642-50282-8_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43344-6

  • Online ISBN: 978-3-642-50282-8

  • eBook Packages: Springer Book Archive

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