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              <p>In the context of shape optimization by the level-set method, we address some new problems : Multiple eigenvalue optimization, robust compliance optimization and buckling load optimization. We also solve two important numerical issues via the bubble method and the velocity regularisation method. This Ph-D thesis also contains a chapter that unveils some of the most important numerical problems that arise when using the level-set method and the numerical tricks that solve these issues.</p>
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              <p>Dans le contexte de l'optimisation de formes par la mé́thode des courbes de niveaux, nous nous inté́ressons à certains nouveaux problèmes : l'optimisation de valeurs propres multiples, l'optimisation de la compliance robuste et l'optimisation du critère de flambement. Nous ré́solvons aussi deux importants problèmes numériques par le couplage avec le gradient topologique et la m ́thode de régularisation de la vitesse. Nous proposons aussi dans cette thèse un chapitre destiné à montrer les probèmes numériques propres à la méthode des courbes de niveaux et nous montrons les "trucs" numériques utilisés pour résoudre ces problèmes.</p>
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