Smoothness of the metric projection onto nonconvex bodies in Hilbert spaces
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Correa, Rafael
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Smoothness of the metric projection onto nonconvex bodies in Hilbert spaces
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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.
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URI: https://repositorio.uchile.cl/handle/2250/169277
DOI: 10.1016/j.jmaa.2016.08.064
ISSN: 10960813
0022247X
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Journal of Mathematical Analysis and Applications, Volumen 457, Issue 2, 2018, Pages 1307-1332
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