Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 45, pp. 1-13.

Title: Convergence results for a class of abstract continuous 
       descent methods
       
Authors: Sergiu Aizicovici (Ohio Univ., Athens, OH, USA)
         Simeon Reich (Technion Inst. of Technology, Israel)
	 Alexander J. Zaslavski (Technion Inst. of Technology, Israel)

Abstract: 
 We study continuous descent methods for the minimization of 
 Lipschitzian functions defined on a general Banach space. 
 We establish convergence theorems for those methods which 
 are generated by approximate solutions to evolution equations 
 governed 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 January 7, 2004. Published March 30, 2004.
Math Subject Classifications: 37L99, 47J35, 49M99, 54E35, 54E50, 54E52, 90C25.
Key Words: Complete metric space;  descent method;  Lipschitzian function; 
           porous set; regular vector field.