Geodesic
Epigraphical Characterization of Uniformly Lower Regular Functions in Hilbert Spaces
Journal of convex analysis, Tome 30 (2023) no. 4, pp. 1139-1153
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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.
Classification : 49J52, 49J53
Mots-clés : Prox-regular set, uniformly prox-regular set, primal lower nice function, proximal normal, distance function, metric projection mapping, Hilbert space 
@article{JCA_2023_30_4_JCA_2023_30_4_a2,
     author = {M. Konstantinov and N. Zlateva},
     title = {Epigraphical {Characterization} of {Uniformly} {Lower} {Regular} {Functions} in {Hilbert} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {1139--1153},
     year = {2023},
     volume = {30},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_4_JCA_2023_30_4_a2/}
}
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M. Konstantinov; N. Zlateva. Epigraphical Characterization of Uniformly Lower Regular Functions in Hilbert Spaces. Journal of convex analysis, Tome 30 (2023) no. 4, pp. 1139-1153. http://geodesic.mathdoc.fr/item/JCA_2023_30_4_JCA_2023_30_4_a2/