Suboptimality Theorems in Optimal Control

  • Andreas Hamel
Part of the International Series of Numerical Mathematics book series (ISNM, volume 124)


Necessary optimality conditions are statements about nothing if an optimal solution does not exist. Therefore it makes sense to embed such conditions in a general framework which excludes the possibility of empty (even false) assertions all the more as the assumptions for existence results are much stronger than those for necessary optimality conditions. We call such a framework suboptimality theorem and exemplify it by a simple problem of optimal control. Furthermore, we investigate the set of suboptimal solutions by means of a new theorem about the approximation of measurable by simple functions.


Optimal Control Problem Existence Result Simple Function Optimal Control Theory Suboptimal Solution 
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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Andreas Hamel
    • 1
  1. 1.Fachbereich Mathematik u. InformatikMartin-Luther-Universität Halle-WittenbergHalle/S.Germany

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