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Displaying similar documents to “Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints”

Mesh-independence and preconditioning for solving parabolic control problems with mixed control-state constraints

Michael Hintermüller, Ian Kopacka, Stefan Volkwein (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

The SQP method for control constrained optimal control of the Burgers equation

Fredi Tröltzsch, Stefan Volkwein (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical...

Convergence of the Lagrange-Newton method for optimal control problems

Kazimierz Malanowski (2004)

International Journal of Applied Mathematics and Computer Science

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Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited....

A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems

Michael Hintermüller, Irwin Yousept (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

The SQP method for control constrained optimal control of the Burgers equation

Fredi Tröltzsch, Stefan Volkwein (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

A Lagrange–Newton–SQP method is analyzed for the optimal control of the Burgers equation. Distributed controls are given, which are restricted by pointwise lower and upper bounds. The convergence of the method is proved in appropriate Banach spaces. This proof is based on a weak second-order sufficient optimality condition and the theory of Newton methods for generalized equations in Banach spaces. For the numerical realization a primal-dual active set strategy is applied. Numerical...