Analyse des problèmes de forme par la dérivation des minimax
Delfour, M.-C. ; Zolésio, J.-P.
Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989), p. 211-227 / Harvested from Numdam
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Publié le : 1989-01-01
@article{AIHPC_1989__S6__211_0,
     author = {Delfour, M.-C. and Zol\'esio, Jean-Paul},
     title = {Analyse des probl\`emes de forme par la d\'erivation des minimax},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {S6},
     year = {1989},
     pages = {211-227},
     mrnumber = {1019115},
     zbl = {0696.49008},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPC_1989__S6__211_0}
}

Delfour, M.-C.; Zolésio, J.-P. Analyse des problèmes de forme par la dérivation des minimax. Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989) pp. 211-227. http://gdmltest.u-ga.fr/item/AIHPC_1989__S6__211_0/

J.P. Aubin [1], L'analyse non linéaire et ses motivations économiques, Masson, Paris, New York, 1984. | MR 754997 | Zbl 0551.90001

N.V. Banichuk [1], Optimization of the Shapes of Elastic Bodies, Nauka, Moscow, 1980 (Engl. Transl. 1984).

J. Cea [1], Conception optimale ou identification de formes. Calcul rapide de la dérivée directionnelle de la fonction coût, R.A.I.R.O. 20 (1986), 371-402. | Numdam | MR 862783 | Zbl 0604.49003

[2], Problems of Shape Optimal Design, in "Optimization of Distributed Parameter Structures", Vol. Il, pp. 1005-1048, Sijthoff and Noordhoff, Alphen aan den Rijn, Netherlands 1980. | Zbl 0517.73096

[3], Numerical Methods of Shape Optimal Design, in "Optimization of distributed parameter structures", E.J. Haug and J. Céa, eds.,pp. 1049-1087, Sijthoff and Noordhoff, Alphen aan den Rijn, Netherlands 1980. | Zbl 0517.73095

R. Correa and A. Seeger [1], Directional derivatives of a minimax function, Nonlinear Analysis, Theory, Methods and Applications 9 (1985), 13-22. | MR 776359 | Zbl 0556.49007

M.C. Delfour and J.P. Zolesio[ 1], Dérivation d'un Min Max et application à la dérivationpar rapport au contrôle d'une observation non différentiable de l'état, C.R. Acad. Sc. Paris 302, Sér. I (1986), 571-574. | MR 844159 | Zbl 0589.49006

[2],, Differentiability of a Min Max and Application to Optimal Control and Design Problems, Part I and II, in "Control Problems for Systems Described as Partial Differential Equations and Applications", I. Lasiecka and R. Triggiani, eds., part I pp. 204-219, part II pp. 220-229, Springer Verlag, New-York, 1987. | MR 910518 | Zbl 0633.49005

[3], Shape Sensitivity Analysis via Min Max Differentiability, SIAM J. on Control and Optim., à paraître. | Zbl 0654.49010

[4], Further developments in shape sensitivity analysis via a penalization method, in "Boundary Control and Boundary Variations", J.P. Zolésio, ed., Springer Verlag, New York, à paraître.

[5], Shape sensitivity analysis via a penalization method, Annali di Matematica Pura i Applicata, à paraître.

K. Dems and Z. Oz [1], Variational approach by means of adjoint systems to structural optimization and sensitivity analysis, Part 2. Structure shape variations, Int. J. of Solids and Structures 20 (1984), 527-552. | MR 763092 | Zbl 0577.73093

V.F. Dem'Yanov [1], Differentiability of a Maximin function. I, USSR Comp. Math. and Math.Phys. 8 (1968), 1-15 (transl from Z. Vychisl. Mat. i Mat. Fiz. 8 (1968), 1186-1195). | Zbl 0218.90050

I. Ekeland and R. Temam [1], Analyse convexe et problèmes variationnels, Dunod,Gauthier -Villars, Paris, Bruxelles, Montréal, 1974. | MR 463993 | Zbl 0281.49001

R.H. Gallagher and O.C. Zienkiewicz [1], Optimum structural design theory and applications, John Wiley and Sons, 1972; Springer Verlag, Berlin 1973. | MR 1602135 | Zbl 0291.73049

E.J. Haug [1], A review of Distributed Parameter Structural Optimization Literature, in"Optimization of Distributed Parameter Structures", Vol. I, pp. 3-74, (cf. Haug and Céa [1 ]). | MR 690959

E.J. Haug and J.S. Arora [1], Applied Optimal Design, Wiley-Interscience, New York,1979.

E.J. Haug and J. Cea [1], Optimization of Distributed Parameter Structures, Vol. I and II,Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands, Rockville, Maryland, USA, 1981. | MR 690958 | Zbl 0511.00034

E.J. Haug , K.K. Choi and V. Komkov[1], Design Sensitivity Analysis of Structural Systems, Academic Press, New York, 1986. | MR 860040 | Zbl 0618.73106

A. Myslinski and J. Sokolowski [1], Nondifferentiable optimization problems for elliptic problems, SIAM J. Control and Optimization 23 (1984), 632-648. | MR 791892 | Zbl 0571.49010

O. Pironneau [1], Optimal Design for Elliptic Systems, Springer Verlag, New York, 1984. | MR 725856 | Zbl 0534.49001

W. Prager [1], Introduction to Structural Optimization, Courses and Lectures: International Centre for Mechanical Sciences, Udine, No 212, Springer Verlag, Vienna, 1974. | MR 441063 | Zbl 0325.73001

G.I.N. Rozvany [1], Optimal Design of Flexural Systems, Pergamon Press, New York, 1976.

A. Sawczuk and Z. Oz [1], Optimization in Structural Design, Springer Verlag, New York, 1975. | Zbl 0309.00033

J. Sokolowski [1], Optimal control in coefficients of boundary value problems with unilateral constraints, Bull. Pol. Acad. Sc. Tech. Sc. 31 (1983), 71-81. | Zbl 0544.49005

J. Sokolowski and J.P. Zolesio [1], Dérivée par rapport au domaine de la solution d'un problème unilatéral, C.R. Acad. Sc. Paris 301 (1985), Sér. I, pp. 103-106. | MR 799603 | Zbl 0605.35028

[2]. Shape sensitivity analysis of an elasto-plastic torsion problem, Bull. Pol. Acad. Sc. Tech. Sc. 33 (1985), 579-586. | Zbl 0595.73098

A. Souissi [1], Quelques problèmes d'optimisation de formes en hydrodynamique, Thèse de Ph.D., Université Laval, Québec (Québec), Canada, décembre 1986.

J.P. Zolesio [1], Identification de domaine, Thèse de doctorat d'état, Nice, 1979.

[2], Semi-Derivatives of Repeated Eigenvalues, in "Optimization of Distributed Parameter Structures", Vol. II, J. Haug and J. Cea, eds, pp. 1457-1473, Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands, Rockville, Maryland, USA, 1981. | Zbl 0518.73086

[3], An optimal design procedure for optimal control support, in "Convex Analysis and its Applications", A. Auslender, ed., pp.207-219, Springer Verlag, Berlin, Heidelberg ,New-York, 1977. | MR 513446