Displaying similar documents to “Extremal Problems - Past and Present”

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....

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...

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

Eduardo Casas (2008)

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...

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

Michael Hintermüller, Ian Kopacka, Stefan Volkwein (2009)

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...