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Abstract

This paper treats stability theory for optimization problems of the following type: Minimize (p,x) subject to x ∊ F(φ), where p ∊ IRm and F(φ) is a non-void, closed, convex subset of IRm for φ ∊ Φ which is a topological space. We investigate upper and lower semicontinuous dependence of the set of optimal solutions on (p,φ). The obtained results imply piecewise continuity of time-optimal controls of certain control systems governed by ordinary differential equations.

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References

  1. 1.
    Brosowski,B.: Parametric approximation and optimization. Amsterdam, North Holland, to appear.Google Scholar
  2. 2.
    Damm,H; Kopielski,T.: Einige Anwendungen der linearen parametrischen Optimierung bei der Untersuchung von optimalen Steuerungsproblemen; in: Lommatzsch,K.: Anwendungen der linearen parametrischen Optimierung. Basel-Stuttgart, Birkhäuser 1979.Google Scholar
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    Grünbaum,B.: Convex polytopes. London-New York-Sydney, Inter-science Publishers 1967.zbMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel 1982

Authors and Affiliations

  • Rainer Colgen
    • 1
  • Klaus Schnatz
    • 1
  1. 1.Fachbereich MathematikUniversität Frankfurt/MainFrankfurt/Main -1Federal Republic of Germany

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