Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 24, pp. 1-11.

Title: Two convergence results for continuous descent methods

Authors: Simeon Reich (The Technion-Israel Institute of Technology)
 Alexander J. Zaslavski (The Technion-Israel Institute of Technology)

Abstract: 
  We consider continuous descent methods for the minimization of 
  convex functionals defined on general Banach space. 
  We  establish two convergence results for methods which 
  are generated by regular vector fields.
  Since the complement of the set of regular vector fields is 
  $\sigma$-porous, we conclude that our results apply to most vector 
  fields in the sense of Baire's categories. 
 
Submitted August 5, 2002. Published March 10, 2003.
Math Subject Classifications: 37L99, 47J35, 49M99,  54E50, 54E52, 90C25.
Key Words: Complete metric space; convex function; descent method; porous set; 
           regular vector field