Journal of Convex Analysis 30 (2023), No. 4, 1139--1153
Copyright Heldermann Verlag 2023
Epigraphical Characterization of Uniformly Lower Regular Functions in Hilbert Spaces
Matey Konstantinov
Faculty of Mathematics and Informatics, Sofia University, Bulgaria, Sofia, Bulgaria
mbkonstant@fmi.uni-sofia.bg
Nadia Zlateva
Faculty of Mathematics and Informatics, Sofia University, Bulgaria, Sofia, Bulgaria
zlateva@fmi.uni-sofia.bg
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.
Keywords: Prox-regular set, uniformly prox-regular set, primal lower nice function, proximal normal, distance function, metric projection mapping, Hilbert space.
MSC: 49J52, 49J53
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