We consider the identification of a distributed parameter in an elliptic variational inequality. On the basis of an optimal control problem formulation, the application of a primal-dual penalization technique enables us to prove the existence of multipliers giving a first order characterization of the optimal solution. Concerning the parameter we consider different regularity requirements. For the numerical realization we utilize a complementarity function, which allows us to rewrite the optimality...
We consider the identification of a distributed parameter in an elliptic
variational inequality. On the basis of an optimal control problem
formulation, the application of a primal-dual penalization
technique enables us to prove the existence
of multipliers giving a first order characterization of the optimal solution.
Concerning the parameter we consider different
regularity requirements. For the numerical realization we utilize a complementarity function,
which allows us to rewrite the optimality...
A numerically inexpensive globalization strategy of sequential quadratic programming methods (SQP-methods) for control of the instationary Navier Stokes equations is investigated. Based on the proper functional analytic setting a convergence analysis for the globalized method is given. It is argued that the a priori formidable SQP-step can be decomposed into linear primal and linear adjoint systems, which is amenable for existing CFL-software. A report on a numerical test demonstrates the feasibility...
Sensitivity analysis (with respect to the regularization parameter)
of the solution of a class of regularized state constrained
optimal control problems is performed. The theoretical results are
then used to establish an extrapolation-based numerical scheme for
solving the regularized problem for vanishing regularization
parameter. In this context, the extrapolation technique provides
excellent initializations along the sequence of reducing
regularization parameters. Finally, the favorable numerical
behavior...
A numerically inexpensive globalization strategy of sequential quadratic programming
methods (SQP-methods) for control of the instationary Navier Stokes equations is investigated.
Based on the proper functional analytic setting a convergence analysis for the globalized method
is given. It is argued that the formidable SQP-step can be decomposed into linear primal
and linear adjoint systems, which is amenable for existing CFL-software. A report on a numerical
test demonstrates the feasibility...
Optimal control problems for the heat equation with pointwise bilateral control-state constraints are considered. A locally superlinearly convergent numerical solution algorithm is proposed and its mesh independence is established. Further, for the efficient numerical solution reduced space and Schur complement based preconditioners are proposed which take into account the active and inactive set structure of the problem. The paper ends by numerical tests illustrating our theoretical findings and...
Optimal control problems for the heat equation with pointwise
bilateral control-state constraints are considered. A locally
superlinearly convergent numerical solution algorithm is proposed
and its mesh independence is established. Further, for the
efficient numerical solution reduced space and Schur complement
based preconditioners are proposed which take into account the
active and inactive set structure of the problem. The paper ends
by numerical tests illustrating our theoretical findings and
comparing...
We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...
We present an error analysis of adaptive finite
element approximations of distributed control problems for second
order elliptic boundary value problems under bound constraints on
the control. The error analysis is based on a residual-type error estimator that consists of edge and element
residuals. Since we do not assume any regularity of the data of
the problem, the error analysis further invokes data oscillations.
We prove reliability and efficiency of the error estimator and
provide a bulk...
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