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- ItemSufficient 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, ArndWe 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
- ItemSecond order sufficient optimality conditions for parabolic optimal control problems with pointwise state constraints(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Krumbiegel, Klaus; Rehberg, JoachimIn this paper we study optimal control problems governed by semilinear parabolic equations where the spatial dimension is two or three. Moreover, we consider pointwise constraints on the control and on the state. We formulate first order necessary and second order sufficient optimality conditions. We make use of recent results regarding elliptic regularity and apply the concept of maximal parabolic regularity to the occurring partial differential equations.