Existence Results for Some Nonconvex Optimization Problems Governed by Nonlinear Processes

  • Tomáš Roubíček
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 124)


Optimal control problems with nonlinear equations usually do not possess optimal solutions. Nevertheless, if the cost functional is uniformly concave with respect to the state, the solution may exist. Using the Balder’s technique based on a Young-measure relaxation, Bauer’s extremal principle and investigation of extreme Young measures, the existence is demonstrated here for the case of nonlinear ordinary and partial differential equations.


Optimal Control Problem Extreme Point Multivalued Mapping Young Measure Pontryagin Maximum Principle 
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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Tomáš Roubíček
    • 1
  1. 1.Institute of Information Theory and Automation, Academy of SciencesMathematical Institute, Charles UniversityCzech Republic

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