
Journal of Convex Analysis 29 (2022), No. 3, 795806 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 semicontinuity, normed space, residual set, strict convexity, uniformity. MSC: 46N10, 54E50, 54E52. [ Fulltextpdf (119 KB)] for subscribers only. 