Journal of Convex Analysis 29 (2022), No. 3, 795--806
Copyright Heldermann Verlag 2022
Residuality Properties of Certain Classes of Convex Functions on Normed Linear Spaces
Kay Barshad
Dept. of Mathematics, The Technion -- Israel Institute of Technology, Haifa, Israel
kaybarshad@campus.technion.ac.il
Simeon Reich
Dept. of Mathematics, The Technion -- Israel Institute of Technology, Haifa, Israel
sreich@technion.ac.il
Alexander J. Zaslavski
Dept. of Mathematics, The Technion -- Israel Institute of Technology, Haifa, Israel
ajzasl@technion.ac.il
We study the existence of residual sets of certain classes of convex functions on a normed linear space. Such sets play an important role in many optimization algorithms for which elements of a certain class can be used as good approximants of given convex functions and thus the abundance of such elements is crucial for the aforementioned algorithms.
Keywords: Baire category, convex function, local uniform convexity, lower semi-continuity, normed space, residual set, strict convexity, uniformity.
MSC: 46N10, 54E50, 54E52.
[ Fulltext-pdf (119 KB)] for subscribers only.