Displaying similar documents to “Asymptotics of an optimal compliance-location problem”

Optimization of the shape and the location of the actuators in an internal control problem

Antoine Henrot, Hervé Maillot (2001)

Bollettino dell'Unione Matematica Italiana

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Consideriamo un corpo Ω sottomesso ad una forza esterna data e del quale vogliamo controllare lo spostamento. Cerchiamo un rinforzo per minimizzare un funzionale che dipende dallo spostamento del corpo. L'insieme delle configurazioni ammissibili è un insieme di funzioni caratteristiche di sottodomini (un rinforzo ammissibile è un sottodominio con una rigidezza uguale ad uno) di volume prescritto. In tal caso, si ha bisogno di una versione rilassata del problema di ottimizzazione e si...

An existence result for an interior electromagnetic casting problem

Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2006)

Open Mathematics

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This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.

On an optimal shape design problem in conduction

José Carlos Bellido (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we analyze a typical shape optimization problem in two-dimensional conductivity. We study relaxation for this problem itself. We also analyze the question of the approximation of this problem by the two-phase optimal design problems obtained when we fill out the holes that we want to design in the original problem by a very poor conductor, that we make to converge to zero.

An existence result for a quadrature surface free boundary problem

Mohammed Barkatou, Diaraf Seck, Idrissa Ly (2005)

Open Mathematics

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The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.

Long-term planning versus short-term planning in the asymptotical location problem

Alessio Brancolini, Giuseppe Buttazzo, Filippo Santambrogio, Eugene Stepanov (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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Given the probability measure ν over the given region Ω ⊂ ℝ n , we consider the optimal location of a set Σ composed by n points in Ω in order to minimize the average distance Σ ↦ ∫ Ω dist ( x , Σ ) d ν (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all n points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and...

Local minimizers of functionals with multiple volume constraints

Édouard Oudet, Marc Oliver Rieger (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We study variational problems with volume constraints, , with level sets of prescribed measure. We introduce a numerical method to approximate local minimizers and illustrate it with some two-dimensional examples. We demonstrate numerically nonexistence results which had been obtained analytically in previous work. Moreover, we show the existence of discontinuous dependence of global minimizers from the data by using a -limit argument and illustrate this with numerical computations....