
Journal of Convex Analysis 13 (2006), No. 3, 623632 Copyright Heldermann Verlag 2006 There are Many Totally Convex Functions Dan Butnariu Dept. of Mathematics, University of Haifa, 31905 Haifa, Israel dbutnaru@math.haifa.ac.il Simeon Reich Dept. of Mathematics, Technion  Israel Inst. Technology, 32000 Haifa, Israel sreich@tx.technion.ac.il Alexander J. Zaslavski Dept. of Mathematics, Technion  Israel Inst. Technology, 32000 Haifa, Israel ajzasl@tx.technion.ac.il [Abstractpdf] Let $K$ be a convex subset of a normed linear space and let $R^1$ denote the real line. We show that there are many (in the sense of Baire category) strictly convex and totally convex functions $f \colon K \to R^1$. It is known that the existence of such functions is crucial in numerous optimization algorithms. Keywords: Complete metric space, essentially strictly convex function, generic property, strictly convex function, totally convex function. MSC: 46N10, 52A41, 54E50, 54E52 [ Fulltextpdf (277 KB)] for subscribers only. 