Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 19, pp. 1-7.

Title: Minimizing convex functions by continuous descent methods
       
Authors: Sergiu Aizicovici (Ohio University, Athens, OH, USA)
         Simeon Reich (The Technion-Israel Inst. of Tech., Israel)
	 Alexander J. Zaslavski (The Technion-Israel Inst. of Tech., Israel)

Abstract:
 We study continuous descent methods for minimizing
 convex functions, defined on general Banach spaces, which are
 associated with an appropriate complete metric space of vector
 fields. We show that there exists an everywhere dense open set in
 this space of vector fields such that each of its elements
 generates strongly convergent trajectories.

Submitted June 27, 2009. Published January 28, 2010.
Math Subject Classifications: 37L99, 47J35, 49M99, 54E35, 54E50, 54E52, 90C25.
Key Words: Complete uniform space; convex function; descent method;
           initial value problem; minimization problem.