IJPAM: Volume 32, No. 1 (2006)

A NOTE ON THE MINIMIZATION
OF CONVEX FUNCTIONS

Marina Arav$^1$, Simeon Reich$^2$, Alexander J. Zaslavski$^3$
$^1$Department of Mathematics and Statistics
Georgia State University
Atlanta, GA 30303, USA
e-mail: matmxa@langate.gsu.edu
$^{2,3}$Department of Mathematics
The Technion-Israel Institute of Technology
Haifa, 32000, ISRAEL
$^2$e-mail: sreichtx.technion.ac.il
$^3$e-mail: ajzasltx.technion.ac.il


Abstract.We consider a complete metric space of Lipschitz mappings, acting on a bounded, closed and convex subset of a Banach space, which share a common convex Lyapunov function $f$. We show that the iterates of a generic element taken from this space converge (at an exponential rate) to the point where $f$ attains its minimum.

Received: September 21, 2006

AMS Subject Classification: Banach space, complete metric space, convex function, generic property, Lipschitz mapping, Lyapunov function, sharp minimum

Key Words and Phrases: 49M99, 54E35, 54E52, 90C25, 90C48

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 32
Issue: 1