Optimal Control of Obstacle Problems:  Existence of Lagrange
Multipliers

Maïtine Bergounioux; Fulbert Mignot

Displaying similar documents to “Optimal Control of Obstacle Problems: Existence of Lagrange Multipliers ”

Optimal control of obstacle problems : existence of Lagrange multipliers

Maïtine Bergounioux, Fulbert Mignot (2000)

ESAIM: Control, Optimisation and Calculus of Variations

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Optimal control of linear bottleneck problems

M. Bergounioux, F. Troeltzsch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The regularity of Lagrange multipliers for state-constrained optimal control problems belongs to the basic questions of control theory. Here, we investigate bottleneck problems arising from optimal control problems for PDEs with certain mixed control-state inequality constraints. We show how to obtain Lagrange multipliers in L spaces for linear problems and give an application to linear parabolic optimal control problems.

Optimal control in some variational inequalities

F. Mignot, J. P. Puel (1985)

Banach Center Publications

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Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints

Anton Schiela, Daniel Wachsmuth (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In the article an optimal control problem subject to a stationary variational inequality is investigated. The optimal control problem is complemented with pointwise control constraints. The convergence of a smoothing scheme is analyzed. There, the variational inequality is replaced by a semilinear elliptic equation. It is shown that solutions of the regularized optimal control problem converge to solutions of the original one. Passing to the limit in the optimality system of the regularized...

On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints

Ira Neitzel, Fredi Tröltzsch (2008)

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Unmaximized inclusion necessary conditions for nonconvex constrained optimal control problems

Maria do Rosário de Pinho, Maria Margarida Ferreira, Fernando Fontes (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Necessary conditions of optimality in the form of Unmaximized Inclusions (UI) are derived for optimal control problems with state constraints. The conditions presented here generalize earlier optimality conditions to problems that may be nonconvex. The derivation of UI-type conditions in the absence of the convexity assumption is of particular importance when deriving necessary conditions for constrained problems. We illustrate this feature by establishing, as an application, optimality...