Voir la notice de l'article provenant de la source Cambridge University Press
Jourani, A.; Thibault, L. Extensions Of Subdifferential Calculus Rules in Banach Spaces. Canadian journal of mathematics, Tome 48 (1996) no. 4, pp. 834-848. doi: 10.4153/CJM-1996-042-1
@article{10_4153_CJM_1996_042_1,
author = {Jourani, A. and Thibault, L.},
title = {Extensions {Of} {Subdifferential} {Calculus} {Rules} in {Banach} {Spaces}},
journal = {Canadian journal of mathematics},
pages = {834--848},
year = {1996},
volume = {48},
number = {4},
doi = {10.4153/CJM-1996-042-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-042-1/}
}
TY - JOUR AU - Jourani, A. AU - Thibault, L. TI - Extensions Of Subdifferential Calculus Rules in Banach Spaces JO - Canadian journal of mathematics PY - 1996 SP - 834 EP - 848 VL - 48 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-042-1/ DO - 10.4153/CJM-1996-042-1 ID - 10_4153_CJM_1996_042_1 ER -
[1] 1. Aubin, J.P., Lipschitz behaviour of solutions to convex minimization problems, Math. Oper., Res. 9(1984), 87–111. Google Scholar
[2] 2. Borwein, J.M., Epi-Lipschitz-like sets in Banach space: Theorems and Examples, Nonlinear, Anal. 11(1987), 1207–1217. Google Scholar
[3] 3. Borwein, J.M. and Strojwas, H.M., Tangential approximations, Nonlinear, Anal. 9(1985), 1347–1366. Google Scholar
[4] 4. Clarke, F.H., Necessary conditions for nonsmooth problems in optimal control and the calculus of variations, Thesis, University of Washington, Seattle (1973). Google Scholar
[5] 5. Clarke, F.H., A new approach to Lagrange multipliers, Math. Oper., Res. 1(1976), 165–174. Google Scholar
[6] 6. Clarke, F.H., Optimization and Nonsmooth Analysis, John Wiley, New York (1983). Google Scholar
[7] 7. Clarke, F.H. and Raissi, N., Formules d'intersection en analyse non lisse, Ann. Sci. Math., Quebec, 14(1990), 121–129. Google Scholar
[8] 8. Dolecki, S., Tangency and differentiation: some applications of convergence, Theory, Ann. Mat. Pura, Appl. 130(1982), 235–255. Google Scholar
[9] 9. El, B. Abdouni and Thibault, L., Lagrange multipliers for Pareto nonsmooth programming problems in Banach spaces,, Optimization 26(1992), 277–285. Google Scholar
[10] 10. Ioffe, A.D., Nonsmooth analysis: differential calculus of non-differentiable mappings, Trans. Amer. Math., Soc. 266(1981), 1–56. Google Scholar
[11] 11. Ioffe, A.D., Approximate subdifferentials and applications. I: The finite dimensional theory, Trans. Amer. Math., Soc, 281(1984), 389–416. Google Scholar
[12] 12. Ioffe, A.D., Approximate subdifferentials and applications II: Functions on locally convex spaces,, Mathematika, 33(1986), 111–128. Google Scholar
[13] 13. Ioffe, A.D., Approximate subdifferentials and applications III: The metric theory,, Mathematika, 36(1989), 1–38. Google Scholar
[14] 14. Jourani, A. and Thibault, L., Metric regularity for strongly compactly Lipschitzian mappings, Nonlinear Anal., to appear. Google Scholar
[15] 15. Jourani, A., The use of metric graphical regularity in approximate subdifferential calculus rules infinite dimensions,, Optimization 21(1990), 509–519. Google Scholar
[16] 16. Jourani, A., Approximate subdifferential of composite functions, Bull. Austral. Math., Soc, 47(1993), 1–13. Google Scholar
[17] 17. Kelley, J.L., General topology, Springer-Verlag, New York, (1975). Google Scholar
[18] 18. Ya, A. Kruger, Properties of generalized differentials, Sib. Math., J. 26(1985), 1822–1832. Google Scholar
[19] 19. Ya, A. Kruger and Mordukhovich, B.S., Extreme points and the Euler equation in nondifferentiable optimization problems, Dokl. Akad. Nauk., BSSR, 24(1980), 684–687. Google Scholar
[20] 20. Loewen, P.D., Limits ofFrechet normals in nonsmooth analysis, In: Optimization and Nonlinear Analysis (eds. Ioffe, A., Marcus, M. and Reich, S.), Pitman Research Notes in Mathematics Series, Great Britain (1992). Google Scholar
[21] 21. Mordukhovich, B.S., Maximum principle in the problem of time optimal control with nonsmooth constraints, J. Appl. Math., Mech., 40(1976), 960–969. Google Scholar
[22] 22. Mordukhovich, B.S., Nonsmooth analysis with nonconvex generalized differentials and adjoint mappings, Dokl. Akad. Nauk., BSSR, 28(1984), 976–979. Google Scholar
[23] 23. Mordukhovich, B.S., Approximation Methods in Problems of Optimization and Control, Nauka, Moscow (1988). Google Scholar
[24] 24. Radstrom, H., An imbedding theorem for spaces of convex sets, Proc Amer. Math., Soc, 3(1952), 165–169. Google Scholar
[25] 25. Rockafellar, R.T., Generalized directional derivatives and subgradients of nonconvex functions, Canad. J., Math. 32(1980), 257–280. Google Scholar
[26] 26. Mordukhovich, B.S., Directionally Lipschitzian functions and subdifferential calculus, Proc London Math., Soc, 39(1979), 331–355. Google Scholar
[27] 27. Mordukhovich, B.S., Extensions of subgradient calculus with applications to optimization, Nonlinear, Anal. 9(1985), 665–698. Google Scholar
[28] 28 Thibault, L., Subdifferentials of compactly Lipschitzian vector valued functions, Ann. Mat. Pura Appl. 125(1980), 157-192. Google Scholar
[29] 29 Ward, D. E. and Borwein, J. M., Nonsmooth calculus infinite dimensions, SIAM J. Control Optim. 25(1987), 1312-1340. Google Scholar
Cité par Sources :