Subdifferential regularity of directionally lipschitzian functions

Canadian Mathematical Bulletin

Volumn 43, Issue 1, 2000, Pages 25-36

  Bounkhel, M ^a   Thibault, L ^a  

^a UNIV MONTPELLIER   (France)

Author keywords

Directional regularity; Directionally lipschitzian functions; Subdifferential regularity

Indexed keywords

EID: 0034147145     PISSN: 00084395     EISSN: None     Source Type: Journal    
DOI: 10.4153/CMB-2000-004-5     Document Type: Article

References (16)

1. F. H. Clarke, Necessary conditions for nonsmooth problems in optimal control and the calculus of variations. Thesis, University of Washington, Seattle, 1973.
2. _, A new approach to Lagrange multipliers. Math. Oper. Res. 1(1976), 97-102.
3. J. Diestel, Sequences and series in Banach spaces. Graduate Texts in Math. 92, Springer-Verlag, 1984.
4. J. B. Hiriart-Urruty, Miscellanies on nonsmooth analysis and optimization. Written version of talk in Sopron, Hungary, 1984.
5. A. Ioffe, Approximate subdifferentials and applications 1: The finite dimensional theory. Trans. Amer. Math. Soc. 281(1984), 389-416.
6. A. Jofré and L. Thibault, D-representation of subdifferentials of directionally Lipschitzian functions. Proc. Amer. Math. Soc. 110(1990), 117-123.
7. A. B. Levy, R. A. Poliquin and L. Thibault, Partial extensions of Attouch's theorem with applications to proto-derivatives of subgradient mappings. Trans. Amer. Math. Soc. 347(1995), 1269-1294.
8. J. P. Penot, Calcul sous-différentiel et optimization. J. Funct. Anal. 27(1978), 248-276.
9. R. R. Phelps, Monotone operators, convex functions and differentiability. 2nd edition, Lecture Notes in Math. 1364, Springer-Verlag, 1993.
10. R. A. Poliquin, Integration of subdifferentials of nonconvex functions. Nonlinear Anal. 17(1991), 385-398.
11. R. T. Rockafellar, Generalized directional derivatives and subgradients of nonconvex functions. Canad. J. Math 39(1980), 257-280.
12. _, Directionally Lipschitzian functions and subdifferential calculus. Proc. London Math. Soc. 39(1979), 331-355.
13. _, Convex Analysis. Princeton Univ. Press, Princeton, NJ, 1970.
14. L. Thibault, A note on the Zagrodny mean value theorem. Optimization 35(1995), 127-130.
15. L. Thibault and D. Zagrodny, Integration of lower semicontinuous functions on Banach spaces. J. Math. Anal. Appl. 189(1995), 33-58.
16. D. Zagrodny, Approximate mean value theorem for upper subderivatives. Nonlinear Anal. 12(1988), 1413-1428.