Displaying similar documents to “Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints”

Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems

Eduardo Casas, Fredi Tröltzsch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Optimal control problems for semilinear elliptic equations with control constraints and pointwise state constraints are studied. Several theoretical results are derived, which are necessary to carry out a numerical analysis for this class of control problems. In particular, sufficient second-order optimality conditions, some new regularity results on optimal controls and a sufficient condition for the uniqueness of the Lagrange multiplier associated with the state constraints are presented. ...

Necessary and sufficient optimality conditions for elliptic control problems with finitely many pointwise state constraints

Eduardo Casas (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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The goal of this paper is to prove the first and second order optimality conditions for some control problems governed by semilinear elliptic equations with pointwise control constraints and finitely many equality and inequality pointwise state constraints. To carry out the analysis we formulate a regularity assumption which is equivalent to the first order optimality conditions. Though the presence of pointwise state constraints leads to a discontinuous adjoint state, we prove that...

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Ira Neitzel, Fredi Tröltzsch (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated...

Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space

Pedro Merino, Fredi Tröltzsch, Boris Vexler (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.