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A Nondifferentiable Approach to Decomposable Optimization Problems with an Application to the Design of Water Distribution Networks

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Advances in Optimization

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 382))

Abstract

We consider the optimization problem

$$ \begin{array}{*{20}{c}} {\inf \,f(q,x)} \\ {subject\,to\,x \in \Omega (q)} \\ {q \in w;} \end{array} $$
((1.1))

here q ∈ℝ n, x ∈ℝ m, f [ℝ n × ℝ m → ℝ] is continuously differentiate, Ω [ℝn ⤳ ℝm] is a proper closed-valued multifunction and ψ is a nonempty compact subset of ℝ n. Problem (1.1) differs from the classical optimal control model due the multivaluedness of Ω which can be now viewed as a multivalued system map.

This work has been supported by the DFG-FSP “Applied Optimization and Control” and by a grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.

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References

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Author information

Authors and Affiliations

  1. Technion-Israel Institute of Technology, Haifa, 32 000, Israel

    A. Ben-Tal & G. Eiger

  2. Czechoslovak Academy of Sciences, 182 08, Prague, CSFR

    J. Outrata

  3. Institute of Mathematics, University of Bayreuth, D-8580, Bayreuth, Germany

    J. Zowe

Authors
  1. A. Ben-Tal
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  2. G. Eiger
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  3. J. Outrata
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  4. J. Zowe
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Mathematik VII Fakultät für Mathematik und Informatik, Universität Mannheim, Schloß, W-6800, Mannheim, Germany

    Werner Oettli

  2. Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Postfach 6980, W-7500, Karlsruhe 1, Germany

    Diethard Pallaschke

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© 1992 Springer-Verlag Berlin Heidelberg

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Ben-Tal, A., Eiger, G., Outrata, J., Zowe, J. (1992). A Nondifferentiable Approach to Decomposable Optimization Problems with an Application to the Design of Water Distribution Networks. In: Oettli, W., Pallaschke, D. (eds) Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51682-5_13

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  • DOI: https://doi.org/10.1007/978-3-642-51682-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55446-2

  • Online ISBN: 978-3-642-51682-5

  • eBook Packages: Springer Book Archive

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