On the Sensivity and Relaxability of Optimal Control Problems Governed by Nonlinear Evolution Equations with State Constraints.
N.S. Papageorgiou, E.P. Avgerinos (1990)
Monatshefte für Mathematik
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N.S. Papageorgiou, E.P. Avgerinos (1990)
Monatshefte für Mathematik
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Ionel Ciuperca, Mohamed El Alaoui Talibi, Mohammed Jai (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.
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...
E. Casas, O. Kavian, J.-P. Puel (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity, such that we cannot expect to have a solution of the state equation for any given control. We then have to speak of pairs (control, state). After having defined a suitable functional class in which we look for solutions, we prove existence of an optimal pair for a large class of cost functions using a non standard compactness argument. Then, we derive a first order optimality...
Eduardo Casas, Fredi Tröltzsch (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper, we carry out the numerical analysis of a distributed optimal control problem governed by a quasilinear elliptic equation of non-monotone type. The goal is to prove the strong convergence of the discretization of the problem by finite elements. The main issue is to get error estimates for the discretization of the state equation. One of the difficulties in this analysis is that, in spite of the partial differential equation has a unique solution for any given control, the...
Barbara Bily (2002)
Applicationes Mathematicae
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Necessary conditions for some optimal control problem for a nonlinear 2-D system are considered. These conditions can be obtained in the form of a quasimaximum principle.
Noriaki Yamazaki (2009)
Banach Center Publications
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In this paper we consider optimal control problems for abstract nonlinear evolution equations associated with time-dependent subdifferentials in a real Hilbert space. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Also, we study approximating control problems of our equations. Then, we show the relationship between the original optimal control problem and the approximating ones. Moreover, we give some applications of our abstract results. ...
J. L. Gámez, J. A. Montero (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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