An augmented Lagrange method for elliptic state constrained optimal control problems

Abstract

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.

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Correspondence to Daniel Wachsmuth.

Additional information

This research was supported by the German Research Foundation (DFG) within the priority program “Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization” (SPP 1962) under Grant Number Wa 3626/3-1.

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Karl, V., Wachsmuth, D. An augmented Lagrange method for elliptic state constrained optimal control problems. Comput Optim Appl 69, 857–880 (2018). https://doi.org/10.1007/s10589-017-9965-y

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Keywords

  • Optimal control
  • State constraints
  • Augmented Lagrange method

Mathematics Subject Classification

  • 49M20
  • 65K10
  • 90C30