Author:
Karl Veronika,Neitzel Ira,Wachsmuth Daniel
Abstract
Abstract
In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the original problem as well as weak convergence of the adjoint states and weak-* convergence of the multipliers associated to the state constraint. Moreover, we show existence of stationary points in arbitrary small neighborhoods of local solutions of the original problem. Additionally, various numerical results are presented.
Funder
Deutsche Forschungsgemeinschaft
Projekt DEAL
Julius-Maximilians-Universität Würzburg
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Control and Optimization
Reference37 articles.
1. Adams, R.A., Fournier, J.J.F.: Sobolev Spaces, Volume 140 of Pure and Applied Mathematics (Amsterdam), 2nd edn. Elsevier/Academic Press, Amsterdam (2003)
2. Birgin, E.G., Martínez, J.M.: Practical Augmented Lagrangian Methods for Constrained Optimization. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2014)
3. Börgens, E., Kanzow, C., Steck, D.: Local and Global Analysis of Multiplier Methods for Constrained Optimization in Banach Spaces. Institute of Mathematics, University of Würzburg, Würzburg (2019). (Preprint)
4. Casas, E.: Control of an elliptic problem with pointwise state constraints. SIAM J. Control Optim. 24(6), 1309–1318 (1986)
5. Casas, E.: Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J. Control Optim. 31(4), 993–1006 (1993)
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