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Subject: Moreau-Yosida approximation ×

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    Existence, uniqueness, and stabilization results for parabolic variational inequalities
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Kröner, Axel; Rautenberg, Carlos N.; Rodrigues, Sérgio
    In this paper we consider feedback stabilization for parabolic variational inequalities of obstacle type with time and space depending reaction and convection coefficients and show exponential stabilization to nonstationary trajectories. Based on a Moreau--Yosida approximation, a feedback operator is established using a finite (and uniform in the approximation index) number of actuators leading to exponential decay of given rate of the state variable. Several numerical examples are presented addressing smooth and nonsmooth obstacle functions.
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    Regularization of state-constrained elliptic optimal control problems with nonlocal radiation interface conditions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Meyer, Christian; Yousept, Irwin
    A state-constrained optimal control problem with nonlocal radiation interface conditions arising from the modeling of crystal growth processes is considered. The problem is approximated by a Moreau-Yosida type regularization. Optimality conditions for the regularized problem are derived and the convergence of the regularized problems is shown. In the last part of the paper, some numerical results are presented.
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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