Tangent sets in some functional spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 42, Issue 5, 2000, Pages 871-886

  Bednarczuk, E ^b   Pierre, M ^a,c   Rouy, E ^d   Sokolowski, J ^a  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

^b SYSTEMS RESEARCH INSTITUTE   (Poland)

^c UNIVERSITÉ PARIS SACLAY   (France)

^d UNIVERSITÉ DE TOURS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL GEOMETRY; CONSTRAINT THEORY; ELASTOPLASTICITY; FUNCTIONS; MATHEMATICAL MODELS; OPTIMIZATION; PLASTICITY; VARIATIONAL TECHNIQUES; VECTORS;

ELASTOPLASTIC CYLINDRICAL ROD; HENCKY PLASTICITY MODEL; NONNEGATIVE FUNCTIONS; SECOND ORDER TANGENT SETS; SHAPE OPTIMIZATION; TANGENT CONE; VARIATIONAL INEQUALITY;

SET THEORY;

EID: 0343878207     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(99)00134-0     Document Type: Article

References (15)

1. J.-P. Aubin, H. Frankowska, Set-Valued Analysis, Birkhauser, Bassel, 1990.
2. A. Ben-Tal, J. Zowe, A unified theory of first and second order conditions for extremum problems in topological vector spaces, Math. Progr. Study. 19 (1982) 39-76.
3. J.F. Bonnans, E. Casas, On the choice of the function spaces for some state-constrained control problems, Numer. Funct. Anal. Optim. 7(4) (1984-1985) 333-348.
4. J.F. Bonnans, E. Casas, Quelques methodes pour le controle optimal de problemes comportant des contraintes sur l'etat, Anals Scient. Univ. Al I. Cuza Tome XXXII (1986) 57-62.
5. E. Casas, Boundary control of semilinear elliptic equations with pointwise state constraints, SIAM, J. Control Optim. 31 (1993) 993-1006.
6. E. Casas, L.A. Fernàndez, Optimal control of semilinear elliptic equations with pointwise constraints on the gradient of the state, Appl. Math. Optim. 27 (1) (1993) 35-56.
7. R. Cominetti, Metric regularity, tangent sets, and second order optimality conditions, Appl. Math. Optim. 21 (1990) 265-287.
8. R. Cominetti, J.-P. Penot, Tangent sets to unilateral sets, CRAS série I 321 (1995) 1631-1636.
9. R. Cominetti, J.-P. Penot, Tangent sets of order one and two to the positive cones of some functional spaces, preprint.
10. A.M. Khludnev, J. Sokolowski, Modelling and control in solid mechanics, International Series of Numerical Mathematics, vol. 122, Birkhauser Verlag, Bassel 1997.
11. J.-P. Penot, Second-order conditions for optimization problems with constraints, SIAM J. Control Optim. 37 (1) (1998) 303-318.
12. K. Piekarski, J. Sokolowski, Shape control of elastic plates, in: P. Kail, I. Lasiecka, M. Polis (Eds.), Proceedings of the 18th IFIP Conference on Systems Modelling and Optimization, Detroit, 1997, Addison-Wesley Longman, to appear.
13. 2(Ω), Nagoya Math. J. 130 (1993) 101-110.
14. M. Rao, J. Sokolowski, Non-linear Balayage and applications, 111. J. Maths, in press.
15. J. Sokolowski, J.-P. Zolesio, Introduction to Shape Optimization, Springer, New York, 1992.