Solving inverse optimal control problems via value functions to global optimality

  • Stephan Dempe
  • Felix Harder
  • Patrick MehlitzEmail author
  • Gerd Wachsmuth


In this paper, we show how a special class of inverse optimal control problems of elliptic partial differential equations can be solved globally. Using the optimal value function of the underlying parametric optimal control problem, we transfer the overall hierarchical optimization problem into a nonconvex single-level one. Unfortunately, standard regularity conditions like Robinson’s CQ are violated at all the feasible points of this surrogate problem. It is, however, shown that locally optimal solutions of the problem solve a Clarke-stationarity-type system. Moreover, we relax the feasible set of the surrogate problem iteratively by approximating the lower level optimal value function from above by piecewise affine functions. This allows us to compute globally optimal solutions of the original inverse optimal control problem. The global convergence of the resulting algorithm is shown theoretically and illustrated by means of a numerical example.


Bilevel optimal control Global optimization Inverse optimal control Optimality conditions Solution algorithm 

Mathematics Subject Classification

49K20 49M20 49N45 90C26 90C48 



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Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceTechnische Universität Bergakademie FreibergFreibergGermany
  2. 2.Institute of Mathematics, Chair of Optimal ControlBrandenburgische Technische Universität Cottbus-SenftenbergCottbusGermany

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