Nonsmooth shape optimization applied to linear acoustics

SIAM Journal on Optimization

Volumn 8, Issue 4, 1998, Pages 989-1006

  Habbal, Abderrahmane ^a  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

Acoustics; Shape optimization; Subgradients

Indexed keywords

EID: 0032352203     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S105262349529581X     Document Type: Article

References (20)

1. P. A. NELSON AND S. J. ELLIOT, Active Control of Sound, Academic Press, New York, 1992.
2. D. DUHAMEL, L'acoustique des problèmes couplés fluide-structure. application au controle actif du son, Thèse de Doctorat, Ecole Nationale des Ponts et Chaussees, Paris, France, 1994.
3. A. MYSLINSKI AND J. SOKOLOWSKI, Nondifferentiable optimization problems for elliptic systems, SIAM J. Control Optim., 23 (1985), pp. 632-648.
4. H. J.-P. MORAND AND R. OHAYON, Interactions Fluides-Structures, RMA 23, Masson, Paris, France, 1992.
5. N. S. TRUDINGER AND D. GILBARG, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
6. B. ROUSSELET, Quelques résultats en optimisation de domaines, Thèse de Doctorat d'Etat, Université de Nice-Sophia Antipolis, Nice, France, 1982.
7. C. LEMARÉCHAL, Nondifferentiable Optimization, Handbooks Oper. Res. Management Sci., North-Holland, Amsterdam, The Netherlands, 1989.
8. J. B. HIRIART-URRUTY AND C. LEMARÉCHAL, Convex Analysis and Minimization Algorithms I and II, Springer-Verlag, Berlin, Heidelberg, 1993.
9. J. S. STRODIOT C. LEMARÉCHAL, AND A. BIHAIN, On a bundle algorithm for nonsmooth optimization, in Nonlinear Programming 4, O. L. Mangasarian, G. L. Meyer, and S. M. Robinson, eds., Academic Press, New York, 1981, pp. 245-282.
10. F. H. CLARKE, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
11. M. M. MAKELA AND P. NEITTAANMAKI, Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control, World Scientific, Singapore, 1992.
12. C. LEMARÉCHAL, Nondifferentiable optimization, in Nonlinear Optimization, L. C. W. Dixon, E. Spedicato, and G. P. Szego, eds., Birkhauser, Basel, 1980, pp. 149-199.
13. J. CEA Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût, MAA Notes, 20 (1986), pp. 371-402.
14. M. MASMOUDI, Outils pour la Conception Optimale de Forme, Thèse d'Etat, University of Nice, Nice, France, 1987.
15. A. HABBAL, Theoretical and numerical study of nonsmooth shape optimization applied to the arch problem, Mech. Structures Mach., 20 (1992), pp. 93-117.
16. J. NECAS, Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris, France, 1967.
17. J. SIMON AND F. MURAT, Sur le Contrôle par un Domaine Géometrique, Thèse d'Etat, Université Paris 6, Paris, France, 1976.
18. O. PIRONNEAU, Optimal Shape Design for Elliptic Systems, Springer-Verlag, Berlin, Heidelberg, New York, 1984.
19. H. SCHRAMM AND J. ZOWE, A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results, SIAM J. Optim., 2 (1992), pp. 121-152.
20. K. C. KIWIEL, Proximity control in bundle methods for convex nondifferentiable optimization, Math. Programming, 46 (1990), pp. 105-122.