Abstract

We provide a characterization of uniformly lower regular functions defined on a Hilbert space. To this end we introduce and study a property we call epi prox-regularity of an epigraph set which slightly differs from the well-known prox-regularity property of a set.

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Keywords

  • Prox-regular set
  • uniformly prox-regular set
  • primal lower nice function
  • proximal normal
  • distance function
  • metric projection mapping
  • Hilbert space

Mathematics Subject Classification

49J52, 49J53

Suggested citation

M. Konstantinov, N. Zlateva. “Epigraphical Characterization of Uniformly Lower Regular Functions in Hilbert Spaces.” Journal of Convex Analysis 30 (2023), No. 4, 1139–1153. https://doi.org/10.68381/jca30051

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Published by Heldermann Verlag, 2023. Rights now held by Banach Press.