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Author: Krumbiegel, Klaus × End date: 2019 × Start date: 2010 × DDC: 510 × Subject: Optimal control × WGL Institute: WIAS ×

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    Sufficient optimality conditions for the Moreau-Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Krumbiegel, Klaus; Neitzel, Ira; Rösch, Arnd
    We develop sufficient optimality conditions for a Moreau-Yosida regularized optimal control problem governed by a semilinear elliptic PDE with pointwise constraints on the state and the control. We make use of the equivalence of a setting of Moreau-Yosida regularization to a special setting of the virtual control concept, for which standard second order sufficient conditions have been shown. Moreover, we compare both regularization approaches within a numerical example
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    Regularization error estimates for semilinear elliptic optimal control problems with pointwise state and control constraints
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Krumbiegel, Klaus; Neitzel, Ira; Rösch, Arnd
    In this paper a class of semilinear elliptic optimal control problem with pointwise state and control constraints is studied. A sufficient second order optimality condition and uniqueness of the dual variables are assumed for that problem. Sufficient second order optimality conditions are shown for regularized problems with small regularization parameter. Moreover, error estimates with respect to the regularization parameter are derived
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    Optimal control of multiphase steel production
    (Berlin ; Heidelberg : Springer, 2019) Hömberg, Dietmar; Krumbiegel, Klaus; Togobytska, Nataliya
    An optimal control problem for the production of multiphase steel is investigated that takes into account phase transformations in the steel slab. The state equations are a semilinear heat equation coupled with an ordinary differential equation, that describes the evolution of the steel microstructure. The time-dependent heat transfer coefficient serves as a control function. Necessary and sufficient optimality conditions for the control problem are derived. For the numerical solution of the control problem, a reduced sequential quadratic programming method with a primal-dual active set strategy is developed. The numerical results are presented for the optimal control of a cooling line in the production of hot-rolled Mo–Mn dual phase steel. © 2019, The Author(s).