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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the metric projection onto prox-regular subsets of Riemannian manifolds


Authors: Seyedehsomayeh Hosseini and Mohamad R. Pouryayevali
Journal: Proc. Amer. Math. Soc. 141 (2013), 233-244
MSC (2010): Primary 49J52, 58C06, 58C20
Published electronically: September 10, 2012
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Abstract: Prox-regular subsets of Riemannian manifolds are introduced. A characterization of prox-regular sets based on the hypomonotonicity of the truncated limiting normal cone is obtained. Moreover, some properties of metric projection mapping and distance function corresponding to the prox-regular sets are presented.


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Additional Information

Seyedehsomayeh Hosseini
Affiliation: Department of Mathematics, University of Isfahan, P. O. Box 81745-163, Isfahan, Iran
Email: somayeh-hosseini@hotmail.com

Mohamad R. Pouryayevali
Affiliation: Department of Mathematics, University of Isfahan, P. O. Box 81745-163, Isfahan, Iran
Email: pourya@math.ui.ac.ir

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11828-3
PII: S 0002-9939(2012)11828-3
Keywords: Prox-regularity, Riemannian manifolds, Clarke subdifferential, proximal subdifferential.
Received by editor(s): December 18, 2010
Published electronically: September 10, 2012
Additional Notes: The second author was partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Iran.
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.