Ferrera Cuesta, Juan and Azagra Rueda, Daniel (2005) Proximal calculus on Riemannian manifolds. Mediterranean journal of mathematics, 2 (4). pp. 437-450. ISSN 1660-5446
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We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold M. We give some applications of this theory, concerning, for instance, a Borwein-Preiss type variational principle on a Riemannian manifold M, as well as differentiability and geometrical properties of the distance function to a closed subset C of M.
|Uncontrolled Keywords:||Proximal subdifferential; Riemannian manifold; Variational principle; Mean value theorem|
|Subjects:||Sciences > Mathematics > Mathematical analysis|
H. Attouch and R.J-B. Wets, A convergence theory for saddle functions. Trans. Amer. Math. Soc. 280 (1983), 1-41.
D. Azagra and M. Cepedello, Uniform approximation of continuous mappings by smooth mappings with no critical points on Hilbert manifolds. Duke Math. J. 124 (2004), 47-66.
D. Azagra and J. Ferrera, Applications of proximal calculus to fixed point theory on Riemannian manifolds. To appear on Nonlinear Anal.
D. Azagra, J. Ferrera and F. L´opez-Mesas, Approximate Rolle’s theorems for the proximal subgradient and the generalized gradient. J. Math. Anal. Appl. 283 (2003), 180-191.
D. Azagra, J. Ferrera and F. L´opez-Mesas, Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds. J. Funct. Anal. 220 (2005), 304-361.
F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory. Grad. Texts in Math. 178, Springer, 1998.
I.Ekeland, Nonconvex minimization problems. Bull. Amer. Math. Soc. (New series) 1 (1979), 443-474.
I.Ekeland, The Hopf-Rinow theorem in infinite dimension. J. Differential Geom. 13 (1978), 287-301.
W. Klingenberg, Riemannian Geometry, de Gruyter Stud. Math., de Gruyter & Co., Berlin-New York, 1982.
C. Mantegazza and A.C. Mennucci, Hamilton-Jacobi equations and distance functions on Riemannian manifolds. Appl. Math. Optim. 47 (2003), 1-25.
|Deposited On:||11 May 2012 07:11|
|Last Modified:||06 Feb 2014 10:18|
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