Equivalence among various derivatives and subdifferentials of the distance function

Journal of Mathematical Analysis and Applications

Volumn 282, Issue 2, 2003, Pages 629-647

  Wu, Zili ^a   Ye, Jane J ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Distance function; Proximal smoothness; Proximal, Fr chet, Dini, and modified Dini subdifferentials; Strict G teaux, and Fr chet derivatives; Uniformly G teaux differentiable norm

Indexed keywords

EID: 0037778834     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00213-0     Document Type: Article

References (9)

1. J.M. Borwein, S.P. Fitzpatrick, J.R. Giles, The differentiability of real functions on normed linear space using generalized subgradients, J. Math. Anal. Appl. 128 (1987) 512-534.
2. J.V. Burke, M.C. Ferris, M. Qian. On the Clarke subdifferential of the distance function of a closed set, J. Math. Anal. Appl. 166 (1992) 199-213.
3. F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.
4. 2 property. J. Convex Anal. 2 (1995) 117-144.
5. F.H. Clarke, Yu. S. Ledyaev, P.R. Wolenski, Proximal analysis and minimization principles, J. Math. Anal. Appl. 196 (1995) 722-735.
6. F.H. Clarke, Yu.S. Ledyaev, R.J. Stern, P.R. Wolenski, Nonsmooth Analysis and Control Theory, in: Graduate Texts in Mathematics, Vol. 178, Springer, New York, 1998.
7. B.D. Craven, D. Ralph, B.M. Glover, Small convex-valued subdifferentials in mathematical programming, Optimization 32 (1995) 1-21.
8. S. Fitzpatrick, Metric projections and the différentiability of distance functions, Bull. Austral. Math. Soc. 22 (1980) 291-312.
9. P. Michel, J.P. Penot, Calcul sous-différentiel pour les fonctions Lipschitziennes et non Lipschitziennes, C. R. Acad. Sci. Paris 298 (1984) 269-272.