Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 44, pp. 1-16.

Title: Optimizing second-order differential equation systems

Authors: Tamas Hajba (Szechenyi Istvan Univ., Gyor, Hungary)

Abstract: 
 In this article we study some continuous versions of the
 Fletcher-Reeves iteration for minimization
 described by a system of second-order differential equations.
 This problem has been studied in earlier papers
 [19, 20] under the assumption that the minimizing
 function is strongly convex. Now instead of the strong convexity,
 only the convexity of the minimizing function will be required.
 We will use  the Tikhonov regularization [28, 29]  to obtain 
 the minimal norm solution as the asymptotically stable
 limit point of the trajectories.

Submitted October 25, 2010. Published March 31, 2011.
Math Subject Classifications: 90C25, 65K05, 34D05.
Key Words: Fletcher-Reeves iteration; second-order differential equation; 
           minimizing trajectory; stationary point in limit; 
	   Lyapunov-type methods.