A Lagrange multiplier method for semilinear elliptic state constrained optimal control problems

Veronika Karl (), Ira Neitzel () and Daniel Wachsmuth ()
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Veronika Karl: Universität Würzburg
Ira Neitzel: Rheinische Friedrich-Wilhelms-Universität Bonn
Daniel Wachsmuth: Universität Würzburg

Computational Optimization and Applications, 2020, vol. 77, issue 3, No 10, 869 pages

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.

Keywords: Optimal control; Semilinear elliptic operators; State constraints; Augmented Lagrange method; 49M20; 65K10; 90C30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10589-020-00223-w

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