Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 13 (2006), No. 3, 623--632Copyright 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 [Abstract-pdf] 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 [ Fulltext-pdf  (277  KB)] for subscribers only.