Computational Optimization and Applications

, Volume 69, Issue 3, pp 857–880 | Cite as

An augmented Lagrange method for elliptic state constrained optimal control problems

  • Veronika Karl
  • Daniel WachsmuthEmail author


In the present work we apply an augmented Lagrange method to solve pointwise state constrained elliptic optimal control problems. We prove strong convergence of the primal variables as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. In addition, we show that the sequence of generated penalty parameters is bounded only in exceptional situations, which is different from classical results in finite-dimensional optimization. In addition, numerical results are presented.


Optimal control State constraints Augmented Lagrange method 

Mathematics Subject Classification

49M20 65K10 90C30 


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Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WürzburgWürzburgGermany

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