Mariano Mateos

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We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The analysis of the approximate control problems is carried out. The uniform convergence of discretized controls to optimal controls is proven under natural assumptions by taking(More)
This paper deals with necessary and sufficient optimality conditions for control problems governed by semilinear elliptic partial differential equations with finitely many equality and inequality state constraints. Some recent results on this topic for optimal control problems based upon results for abstract optimization problems are compared with some new(More)
We obtain error estimates for the numerical approximation of a distributed control problem governed by the stationary Navier–Stokes equations, with pointwise control constraints. We show that the L2-norm of the error for the control is of order h2 if the control set is not discretized, while it is of order h if it is discretized by piecewise constant(More)
We apply Robin penalization to Dirichlet optimal control problems governed by semilinear elliptic equations. Error estimates in terms of the penalization parameter are stated. Error estimates for the numerical approximation of both Dirichlet and Robin optimal control problems are provided and the optimal relation of the penalization and the discretization(More)
We discuss error estimates for the numerical analysis of Neumann boundary control problems. We present some known results about piecewise constant approximations of the control and introduce some new results about continuous piecewise linear approximations. We obtain the rates of convergence in i ^ ( r ) . Error estimates in the uniform norm are also(More)
In this talk we consider the following optimal control problem (P)  minJ(u) = ∫ Ω L(x, yu(x)) dx+ N 2 ∫ Γ u(x) dσ(x) subject to (yu, u) ∈ (L∞(Ω) ∩H(Ω))× L(Γ), α ≤ u(x) ≤ β for a.e. x ∈ Γ, where Γ is a smooth manifold, yu is the state associated to the control u, given by a solution of the Dirichlet problem { −∆y + a(x, y) = 0 in Ω, y = u on Γ. (1) To(More)