Smoothness of the metric projection onto nonconvex bodies in Hilbert spaces
Author
dc.contributor.author
Correa, Rafael
Author
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Salas, David
Author
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Thibault, Lionel
Admission date
dc.date.accessioned
2019-05-31T15:18:56Z
Available date
dc.date.available
2019-05-31T15:18:56Z
Publication date
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2018
Cita de ítem
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Journal of Mathematical Analysis and Applications, Volumen 457, Issue 2, 2018, Pages 1307-1332
Identifier
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10960813
Identifier
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0022247X
Identifier
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10.1016/j.jmaa.2016.08.064
Identifier
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https://repositorio.uchile.cl/handle/2250/169277
Abstract
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Based on a fundamental work of R. B. Holmes from 1973, we study differentiability properties of the metric projection onto prox-regular sets. We show that if the set is a nonconvex body with a Cp+1-smooth boundary, then the projection is Cp-smooth near suitable open truncated normal rays, which are determined only by the function of prox-regularity. A local version of the same result is established as well, namely, when the smoothness of the boundary and the prox-regularity of the set are assumed only near a fixed point. Finally, similar results are derived when the prox-regular set is itself a Cp+1-submanifold.