Proximal calculus on Riemannian manifolds
| dc.contributor.author | Ferrera Cuesta, Juan | |
| dc.contributor.author | Azagra Rueda, Daniel | |
| dc.date.accessioned | 2023-06-20T09:34:02Z | |
| dc.date.available | 2023-06-20T09:34:02Z | |
| dc.date.issued | 2005 | |
| dc.description.abstract | 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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15202 | |
| dc.identifier.doi | 10.1007/s00009-005-0056-4 | |
| dc.identifier.issn | 1660-5446 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/p1q0626q11453542/fulltext.pdf?MUD=MP | |
| dc.identifier.relatedurl | http://www.springerlink.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49922 | |
| dc.issue.number | 4 | |
| dc.journal.title | Mediterranean journal of mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 450 | |
| dc.page.initial | 437 | |
| dc.publisher | BIRKHAUSER VERLAG AG | |
| dc.relation.projectID | BFM2003-06420 | |
| dc.relation.projectID | CT2003-500927 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.986.6 | |
| dc.subject.cdu | 517.518.45 | |
| dc.subject.keyword | Proximal subdifferential | |
| dc.subject.keyword | Riemannian manifold | |
| dc.subject.keyword | Variational principle | |
| dc.subject.keyword | Mean value theorem | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Proximal calculus on Riemannian manifolds | |
| dc.type | journal article | |
| dc.volume.number | 2 | |
| dcterms.references | 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. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 1a91d6af-aaeb-4a3e-90ce-4abdf2b90ac3 | |
| relation.isAuthorOfPublication | 6696556b-dc2e-4272-8f5f-fa6a7a2f5344 | |
| relation.isAuthorOfPublication.latestForDiscovery | 1a91d6af-aaeb-4a3e-90ce-4abdf2b90ac3 |
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