The multidirectional mean value theorem in Banach spaces

Canadian Mathematical Bulletin

Volumn 40, Issue 1, 1997, Pages 88-102

  Radulescu, M L ^a   Clarke, F H ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031092526     PISSN: 00084395     EISSN: None     Source Type: Journal    
DOI: 10.4153/CMB-1997-011-2     Document Type: Article

References (18)

1. J. M. Borwein and D. Preiss, A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions, Trans. Amer. Math. Soc. 303(1987), 517-527.
2. J. M. Borwein and H. M. Strojwas, Proximal analysis and boundaries of closed sets in Banach space, I, Theory, Canad. J. Math. 38(1986), 431-452.
3. _, Proximal analysis and boundaries of closed sets in Banach space, II, Applications, Canad. J. Math. 39(1987), 428-472.
4. F. H. Clarke, Optimization and nonsmooth analysis, Classics Appl. Math. 5, SIAM Publications, Philadelphia, 1990, originally published by Wiley Interscience, New York, 1983.
5. _, Methods of dynamic and nonsmooth optimization, CBMS-NSF Regional Conf. Ser. Appl. Math. 57, SIAM Publications, Philadelphia, 1989.
6. F. H. Clarke and Yu. S. Ledyaev, Mean value inequalities in Hilbert space, Trans. Amer. Math. Soc. 344(1994), 307-324.
7. _, Mean value inequalities, Proc. Amer. Math. Soc. 122(1994), 1075-1083.
8. F. H. Clarke, Yu S. Ledyaev, R. J. Stern, and P. R. Wolenski, Subdifferential and nonlinear analysis, monograph, in preparation.
9. F. H. Clarke, R. J. Stern and P. R. Wolenski, Subgradient criteria for monotonicity, the Lipschitz condition and convexity, Canad. J. Math. 45(1993), 1167-1183.
10. R. Deville, G. Godefroy and V. Zizler, A smooth variational principle with applications to Hamilton-Jacobi equations, Infinite Dimensions, J. Funct. Anal. 111(1993), 197-212.
11. _, Smoothness and renormings in Banach spaces, Pitman Monographs, Surveys Pure Appl. Math. 64, Longman, 1993.
12. R. Deville and E. M. El Haddad, The subdifferential of the sum of two functions in Banach spaces, I. First order case, to appear.
13. J. Diestel, Geometry of Banach spaces-selected topics, Lecture Notes in Math. 485, Springer, 1975.
14. A. D. Ioffe, Proximal analysis and approximate subdifferentials, J. London Math. Soc. (2) 41(1990), 175-192.
15. A. S. Lewis, D. Ralph, A nonlinear duality result equivalent to the Clarke-Ledyaev mean value inequality, Nonlinear Anal., to appear.
16. P. D. Loewen, Optimal control via nonsmooth analysis, CRM Proceedings and Lecture Notes 2, Amer. Math. Soc., Providence, 1993.
17. A. Subbotin, On a property of a subdifferential, Mat. Sb. 1982(1991) 1315-1330; Russian.
18. _, Generalized solutions of first order PDEs: The dynamical optimization perspective, Birkhaüser, to appear.