Variational analysis for a class of minimal time functions in Hilbert spaces

Journal of Convex Analysis

Volumn 11, Issue 2, 2004, Pages 335-361

  Colombo, Giovanni ^a   Wolenski, Peter R ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4544267754     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. P. Albano, P. Cannarsa, C. Sinestrari: Regularity results for the minimum time function of a class of semilinear evolution equations of parabolic type, SIAM J. Control Optimization 38 (2000) 916-946.
2. J. P. Aubin, H. Frankowska: Set-Valued Analysis, Birkhäuser, Boston (1990).
3. M. Bardi: A boundary value problem for the minimal time problem, SIAM J. Control Optimization 27 (1989) 776-785.
4. M. Bounkhel, L. Thibault: On various notions of regularity of sets in nonsmooth analysis, Nonlinear Anal., TMA 48 (2002) 223-246.
5. A. Bressan: On two conjectures by Hájek, Funkc. Ekv. 23 (1980) 221-227.
6. A. Canino: On p-convex sets and geodesics, J. Diff. Equat. 75 (1988) 118-157.
7. n, Trans. Amer. Math. Soc. 353 (2001) 4567-4581.
8. P. Cannarsa, C. Sinestrari: Convexity properties of the minimum time function, Calc. Var. 3 (1995) 273-298.
9. P. Cannarsa, C. Sinestrari: An infinite dimensional time optimal control problem, in: Optimization Methods in Partial Differential Equations, S. Cox, I. Lasiecka (eds.), Contemp. Math. 209, Providence (1997) 29-41.
10. F. H. Clarke: Optimization and Nonsmooth Analysis, Wiley, New York (1983).
11. F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer, New York (1998).
12. 2 property, J. Convex Anal. 2 (1995) 117-144.
13. G. Colombo, V. Goncharov: Variational inequalities and regularity properties of closed sets in Hilbert spaces, J. Convex Anal. 8 (2001) 197-221.
14. G. Colombo, P. R. Wolenski: The subgradient formula for the minimal time function in the case of constant dynamics in Hilbert space, Journal of Global Optimization, in print.
15. I. Ekeland, R. Témam: Convex Analysis and Variational Problems, Classics in Applied Mathematics 28, SIAM, Philadelphia (1999).
16. R. A. Poliquin, R. T. Rockafellar, L. Thibault: Local differentiability of distance functions, Trans. Amer. Math. Soc. 352 (2000) 5231-5249.
17. R. T. Rockafellar, R. J.-B. Wets: Variational Analysis, Springer, Berlin (1998).
18. P. Soravia: Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex Hamiltonians, Comm. Partial Differ. Equations 18 (1993) 1493-1514.
19. P. Soravia: Generalized motion of a front propagating along its normal direction, Nonlinear Anal., TMA 22 (1994) 1247-1262.
20. V. Veliov: Lipschitz continuity of the value function in optimal control, J. Optimization Theory Appl. 94 (1997) 335-363.
21. P. R. Wolenski, Z. Yu: Proximal analysis and the minimal time function, SIAM J. Control Optim. 36 (1998) 1048-1072.