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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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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